Conservation Law Models of Granular Flow

2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 17 Conservation Law Models of Granular Flow Alberto Bressan The Penn State University, USA [email protected] The talk is concerned with a model of granular flow, formulated as a scalar conservation law with nonlocal flux. Recent results will be reviewed, concerning the global existence of smooth solutions, the finite time formation of singularities, and the asymptotic shape of solutions. I shall also present a general result on the global well-posedness of the Cauchy problem, Proved within the framework of semigroup theory. Approximate solutions are here constructed by backward Euler approximations, combined with a projection operator. This is a joint work with Wen Shen. --------------------------------------------------------------------------------------------------------------------Large Time-step and Asymptotic-preserving Numerical Schemes for the Gas Dynamics Equations with Source Terms Christophe Chalons Université Versailles Saint-Quentin-en-Yvelines,France [email protected] We propose a large time-step and asymptotic-preserving scheme for the gas dynamics equations with external forces and friction terms. By asymptotic-preserving, we mean that the numerical scheme is able to reproduce at the discrete level the parabolic-type asymptotic behaviour satisfied by the continuous equations. By large time-step, we mean that the scheme is stable under a CFL stability condition driven by the (slow) material waves, and not by the (fast) acoustic waves as it is customary in Godunov-type schemes. Numerical evidences are proposed and show a gain of several orders of magnitude in both accuracy and efficiency. If time permits, an extension of the method to low-Mach number regimes will be discussed. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 18 Multidimensional Shock Waves and Free Boundary Problems Gui-Qiang G. Chen University of Oxford, UK [email protected] In this talk we will analyze several longstanding, fundamental multidimensional shock problems in mathematical fluid mechanics and related free boundary problems for nonlinear partial differential equations of mixed elliptic-hyperbolic type. These shock problems include supersonic flow onto a solid wedge (Prandtl-Meyer’s problem), shock reflection-diffraction by a concave cornered wedge (von Neumann's conjectures), and shock diffraction by a convex cornered wedge (Lighthill’s problem). Some recent developments and related mathematical challenges in solving these problems will be discussed. Further trends and open problems in this direction will be also addressed. This is based on joint work with M. Bae, M. Feldman, as well as W. Xiang. ---------------------------------------------------------------------------------------------------------------------Global Existence of Small Amplitude Solutions to the Vlasov-Poisson System with Radiation Damping Jing Chen Huazhong University of Science and Technology, China [email protected] In this paper, with some dispersion property and Schauder's fixed point theorem, we establish the existence of a global classical solution to a damped Vlasov-Poisson system in three dimensional space under the assumption that the initial datum is sufficiently small and decays at infinity in phase space. Before this work, only a local solution was obtained for the three dimensional damped Vlasov-Poisson system. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 19 Global Well-posedness in Spatially Critical Besov Space for the Boltzmann Equation Renjun Duan The Chinese University of Hong Kong, China [email protected] The unique global strong solution in the Chemin-Lerner type space to the Cauchy problem on the Boltzmann equation for hard potentials is constructed in perturbation framework. Such solution space is of critical regularity with respect to spatial variable, and it can capture the intrinsic property of the Botlzmann equation. For the proof of global well-posedness, we develop some new estimates on the nonlinear collision term through the Littlewood-Paley theory. ---------------------------------------------------------------------------------------------------------------------Well-posedness for the 2D Boussinesq Type Equations with Super-critical Dissipation Daoyuan Fang Zhejiang University, China [email protected] In this talk we first give the local in time existence of solutions to the 2D incompressible Boussinesq type equations with super-critical dissipation in inhomogeneous Besov spaces, and then presents two blow-up criteria in terms of the velocity and temperature respectively, these blow-up criteria are the improvement of the Lipschitz case, and meanwhile, we also get two blow-up criteria of Boussinesq system with zero viscosity. Finally, we get the global solution if the initial data is small. This is the joint work with C. Qian and T. Zhang. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 20 On the Global Well-posedness of the Inhomogeneous Incompressible Fluid Dynamical System Guilong Gui Northwest University, China [email protected] Consideration in this talk is the global well-posedness of some inhomogeneous incompressible fluid dynamical systems. Without smallness assumption on the variation of the initial density function, we first demonstrate the global well-posedness of the 3-D inhomogeneous incompressible Navier-Stokes equations with highly oscillatory initial velocity field and any initial density function with a positive lower bound. On the other hand, we investigate the effects of inhomogeneous density and electrical conductivity on the well-posedness of the two-dimensional magnetohydrodynamics system (MHD). It is shown that the 2-D inhomogeneous MHD with a constant viscosity is globally well-posed for a generic family of the variations of the initial data and an inhomogeneous electrical conductivity. The talk is based on results obtained jointly with H. Abidi and with P. Zhang. ---------------------------------------------------------------------------------------------------------------------Synchronization of Classical and Quantum Oscillator Systems Seung Yeal Ha Seoul National University, Korea [email protected] In this talk, I will report recent progress on the complete synchronization problem of the classical and quantum oscillator systems appearing in biological and physical complex systems. This is a joint work with Dr. Sun-Ho Choi (NUS). 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 21 Realization in R^3 of Two Types of Riemannian manifolds with negative Gauss curvature Feimin Huang Chinese Academy of Sciences, China [email protected] The realization of abstract 2-D Riemannian manifold in R^3 is a fundamental and challenging problem in the field of differential geometry. The problem is equivalent to solve initial and/or boundary value problems of Gauss-Codazzi systems, which are of nonlinear partial differential equations of mixed elliptic-hyperbolic type. In this talk, we will show the isometric immersion in R^3 of two types of 2-D Riemannian manifolds with negative Gauss curvature. In particular, the result includes two important surfaces-catenoid and helicoid, and does not require any smallness of initial data. ---------------------------------------------------------------------------------------------------------------------Global Well-posedness of Incompressible Elastodynamics in 2D Zhen Lei Fudan University, China [email protected] In this talk I will report our recent result on the global well posedness of classical solutions to system of incompressible elastodynamics in 2D. The system is revealed to be inherently strong linearly degenerate and automatically satisfies a strong null condition, due to the isotropic nature and the incompressible constraint. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 22 Stability of Some Fluid Type Problems Congming Li Shanghai Jiao Tong University, China [email protected] We will focus on the investigation of special structures related to the study of the dynamic stability of the 3D incompressible Euler and Navier-Stokes equations. Some special models have been studied. We will also present some derivations of other models and the stability or instability of these models. ---------------------------------------------------------------------------------------------------------------------Global Wellposedness and Traveling Wave Solutions of PDE Models of Chemotaxis Tong Li The University of Iowa,USA [email protected] We investigate local and global existence, blowup criterion and long time behavior of classical solutions for a system of PDEs derived from the Keller-Segel model describing chemotaxis. Moreover, we establish the existence and the nonlinear stability of large-amplitude traveling wave solutions to the system of nonlinear conservation laws derived from Keller-Segel model. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 23 Global Stability of the Rarefaction Wave of the Vlasov-Poisson-Boltzmann System Shuangqian Liu Jinan University, China [email protected] In this talk, we consider the nonlinear stability of the rarefaction waves of the Vlasov-Poisson-Boltzmann system with slab symmetry in the case where the electron background density satisfies an analogue of the Boltzmann relation. We allows that the electric potential may take distinct constant states at both far-fields. The rarefaction wave whose strength is not necessarily small is constructed through the quasineutral Euler equations coming from the zero-order fluid dynamic approximation of the kinetic system. We prove that the local Maxwellian with macroscopic quantities determined by the quasineutral rarefaction wave is time-asymptotically stable under small perturbations for the corresponding Cauchy problem on the Vlasov-Poisson-Boltzmann system. The main analytical tool is the combination of techniques for the viscous compressible fluid with the self-consistent electric field and the reciprocal energy method based on the macro-micro decomposition of the Boltzmann equation around a local Maxwellian. Both the time decay property of the rarefaction waves and the structure of the Poisson equation play a key role in the analysis. This is a joint work with Professor Renjun Duan ---------------------------------------------------------------------------------------------------------------------Influence of Boundary Conditions on the Qualitative Property of a Reaction Diffusion Equation Bendong Lou Tongji University, China [email protected] We study a reaction diffusion equation         t h , x u f u u xx t 0    with Robin boundary condition     t , bu t , u x 0 0  . When f is an unbalanced bistable nonlinearity we prove a trichotomy result on the long time behavior of the solutions, that is, any solution converges either to 0 (i.e. vanishing), or an active solution (i.e. spreading), or a ground state     t y x V  with finite or infinite shift   t y (i.e. transition). In the last case, we show that   z t y  for some real z when b is large, and for some B , A depending on b and f when b is small. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 24 Non-uniqueness of Weak Solutions to the Rotating Shallow Water Systems Tianwen Luo The Chinese University of Hong Kong, China [email protected] We consider the weak solutions to the the rotating shallow water systems in 2D, and we show the existence of infinitely many global-in-time admissible bounded weak solutions for some piece-wise smooth initial densities and L initial velocities. ---------------------------------------------------------------------------------------------------------------------A Mathematical Analysis of a PDE Model for Biological Network Formation Peter Markowich University of Cambridge, UK [email protected] in collaboration with Jan Haskovec (KAUST) and Benoit Perthame (Paris VI) Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by D. Hu and D. Cai. The model describes the pressure field by a Darcy type equation and the dynamics of the conductance network under pressure force and decay effects with a diffusion rate D representing randomness in the material structure. We prove the existence of global weak solutions and of local mild solutions and study their long term behavior. It turns out that, by energy dissipation, steady states play a central role to understand the pattern formation capacity of the system. We show that for a large diffusion coefficient D, the zero steady state is stable. Patterns occur for small values of D because the zero steady state is Turing unstable in this range; for D = 0 we can exhibit a large class of dynamically stable (in the linearized sense) steady states. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 25 Stability of Oscillatory Traveling Waves for Reaction-diffusion Equation with Time-delay Ming Mei McGill University/Champlain College--Saint-Lambert, Canada [email protected] In this talk, we present our new results on stability of oscillatory traveling waves for a class of reaction-diffusion equations with time-delay. The typical model is the Nicholson’s blowflies equation. When the birth rate function is non-monotone, the equation losses its monotonicity, and the traveling waves are oscillating for a large time-delay. These cause the study totally different from the monotone case, and will be more challenging. By using the technical weighted energy method with some new development, and the Halanay’s inequality, we prove that, for all non-critical monotone/non-monotone traveling waves, they are time-exponentially stable, and for all critical monotone/non-monotone traveling waves, they are time-algebraically stable. Some numerical computations will be also reported, which further confirm and support our theoretical results. ---------------------------------------------------------------------------------------------------------------------Global Dynamics of Heterogeneous Lotka-Volterra Competition-Diffusion Systems Wei-Ming Ni University of Minnesota, USA [email protected] In this talk, I will discuss the joint effects of diffusion and spatial variation on the global dynamics of a classical Lotka-Volterra competition system. A complete understanding of the change in dynamics is obtained in terms of diffusion rates. Various special cases will be discussed to illustrate the findings. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 26 Asymptotic Stability of Stationary Solutions to Symmetric Hyperbolic-Parabolic Systems in Half Space and the Convergence Rate Shinya Nishibata Tokyo Institute of Technology, Japan [email protected] We consider the large-time behavior of solutions to hyperbolic-parabolic coupled systems in the half line. Assuming that the systems admit the entropy function, we may rewrite them to symmetric forms. For the symmetrizable hyperbolic-parabolic systems, we first prove the existence of the stationary solution. We also prove that the stationary solution is time asymptotically stable under a smallness assumption on the initial perturbation. Moreover, we obtain the convergence rate towards the stationary solutions. These theorems for the general hyperbolic-parabolic system cover the compressible Navier-Stokes equation for heat conductive gas. ---------------------------------------------------------------------------------------------------------------------Global Existence and Parabolic Limit of First-order Quasilinear Hyperbolic Systems Yue-Jun Peng Université Blaise Pascal, France [email protected] We consider the Cauchy problem for first-order quasilinear partially dissipative hyperbolic systems with a small parameter. Typically, the small parameter is the relaxation time in physical models. Under stability conditions, we show the global existence of smooth solutions in a uniform neighbourhood of a constant equilibrium state with respect to the parameter. In a slow time, this allows to obtain the global-in-time convergence of the systems to parabolic equations as the parameter goes to zero. For large initial data, the convergence is justified in a uniform local-in-time interval. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 27 Large-time Behaviour of Solutions for a 1D Radiative Model Yuming Qin Donghua University, China [email protected] In this talk, we shall present some recent results on the large-time behaviour of solutions for a 1D radiative model. ---------------------------------------------------------------------------------------------------------------------Entropy Satisfying Finite Volume Schemes for Systems of Conservation Laws Nicolas Seguin Université Pierre et Marie Curie, France [email protected] We consider systems of conservation laws which satisfy classical physical assumptions: Galilean invariance, reversibility of smooth solution and existence of an convex entropy. A common form can be deduced and we use it to construct general numerical schemes. They are based on a relaxation approximation, proved to be nonlinearly stable. The resulting schemes are proved to be entropy satisfying. Thanks to this property, error estimates for strong solutions and convergence towards measure-valued solutions can be obtained. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 28 Propagation of Weak Discontinuities and Characteristic Decompositions in Hyperbolic Systems for Conservation Laws Wancheng Sheng Shanghai University, China [email protected] The propagation of weak discontinuities is an important phenomenon in the theory of hyperbolic partial differential equations. It appears in physics, such as the spread of the wave front in the traveling of the rarefaction waves and the propagation of the wave front which is caused by the abrupt changes on terrain in the shallow water flow, etc. In this paper, by use of the characteristic decomposition method, we give the theory of propagation of weak discontinuities for compressible Euler system. It is proved that the weak discontinuities spread along characteristic curves for the Euler system, including one dimensional polytropic gas flow and two dimensional ideal gas flow, etc. Furthermore, two examples for the Euler system are shown. One is the rarefaction wave in polytropic gas flow and the other is the expansion problem of gas into vacuum in the pseudo-steady flow. (Joint work with Ju Ge) ---------------------------------------------------------------------------------------------------------------------Optimal Partial Regularity of Second Order Parabolic Systems under Controllable Growth Condition Zhong Tan Xiamen University, China [email protected] We consider the regularity for weak solutions of second order nonlinear parabolic systems under controllable growth condition, and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, we get the optimal regularity by the method of A-caloric approximation introduced by Duzaar and Mingione. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 29 Global Dynamics of a Chemotaxis-haptotaxis System Youshan Tao Donghua University, China [email protected] This talk addresses a coupled chemotaxis-haptotaxis system modeling cancer cell invasion of surrounding tissue, which describes the interactions between the cancer cell density, the concentration of a matrix-degrading enzyme (MDE) and the density of extracellular matrix (ECM). In addition to random movement, cancer cells are supposed to bias their movement both towards increasing concentrations of urokinase plasminogen activator by chemotaxis, and towards increasing densities of the non-diffusible ECM through detecting the macromolecules adhered therein by haptotaxis. It is assumed that the cancer cells undergo birth and death in a logistic manner, competing for space with the ECM. The MDE is assumed to be produced by cancer cells, and to diffuse and decay, whereas the ECM is assumed to be degraded upon contact with MDE. We first discuss the global existence and boundedness of the solutions to the system for appropriate parameter conditions. Then we consider the dominance of chemotaxis whenever the initial ECM density is ``small" in certain sense. We next study the asymptotic behavior of solutions when the initial cell density has a positive lower bound in addition to some smallness assumption on initial ECM density. Finally, we briefly review some related results for haptotaxis-only system and for coupled chemotaxis-haptotaxis system. This talk is based on a coupl of joint works with Prof. Michael Winkler at University of Paderborn. ---------------------------------------------------------------------------------------------------------------------The Integral of the Normal, Fluxes over Sets of Finite Perimeter, and Applications to Averaged Shape Optimization Ido Bright and Monica Torres Purdue University, USA [email protected] Given two intersecting sets of finite perimeter, 1 E and 2 E , with unit normals 1  and 2  respectively, we obtain a bound on the integral of 1  over the reduced boundary of 1 E inside 2 E . This bound depends only on the perimeter of 2 E . For any vector feld : n n F  R R with the property that F L  and divF is a (signed) Radon measure, we obtain bounds on the flux of F over the portion of the reduced boundary of 1 E inside 2 E . These results are then applied to averaged shape optimization problems. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 30 Blow-up Phenomena in Nonlinear Parabolic Problems Stella Piro Vernier The University of Cagliari, Italy [email protected] Blow-up solutions to a class of reaction diffusion equations and systems under various boundary conditions are investigated. Under certain conditions on data the blow-up will occur at some finite time and when the blow-up does occur, lower and/or upper bounds are derived. ---------------------------------------------------------------------------------------------------------------------The Glassey Conjecture on Asymptotically Flat Manifolds Chengbo Wang Zhejiang University, China [email protected] In this talk, we will discuss our recent work on the long time existence for small solutions to certain semilinear wave equations of type | | tt t u u u   , posed on asymptotically flat manifolds. This problem is related with the Glassey conjecture. In the flat case (Minkowski spacetime), it is conjectured that the critical index for the problem to admit small global solutions is 1 2 / ( 1) c p n    . It has been verified for spatial dimension two and three, as well as the radial case for all dimensions. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 31 Hydrodynamic Systems for Liquid Crystals Dehua Wang University of Pittsburgh, USA [email protected] The Ericksen-Leslie system and Q-tensor system for flows of nematic liquid crystals will be discussed. Recent results on existence of global solutions, large-time behavior, and incompressible limits will be presented. ---------------------------------------------------------------------------------------------------------------------Optimal Regularity of Boundary Value Problems Lihe Wang Shanghai Jiao Tong University, China [email protected] We will talk about regularity of boundary value problems and particularly about the conditions under which the solution is differentiable. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 32 Stability of Superposition of Two Viscous Shock Waves for the Boltzmann Equation Yi Wang Chinese Academy of Sciences, China [email protected] I will talk about the time-asymptotic stability of a superposition of two viscous shock waves for one-dimensional Boltzmann equation in Eulerian coordinate under the general initial perturbation without the zero total macroscopic mass condition. Roughly speaking, the general perturbation without the zero mass condition will generate not only the shifts on the two viscous shock waves, but also the linear diffusion wave in the linearly degenerate field. Furthermore, the coupled diffusion waves for the macroscopic part are also crucial in the stability analysis. By using the delicate weighted characteristic energy estimates based on the underlying wave structure, we succeed in proving the time-asymptotic stability of a superposition of two viscous shock waves for Boltzmann equation in Eulerian coordinate without the zero initial mass condition. It is noted that this is the first time-asymptotic stability result for the superposition of two waves for Boltzmann equation even though the stability towards a single wave has been well-established. This is a joint work with Teng Wang. ---------------------------------------------------------------------------------------------------------------------Stability of Traveling Waves of a Chemotaxis System Modeling the Initiation of Angiogenesis Zhi-An Wang Hong Kong Polytechnic University, China [email protected] This talk will report the nonlinear stability of large-amplitude traveling waves of a chemotaxis system with singular logarithmic sensitivity describing the initiation of angiogenesis, which partially solve a long-standing open question of the stability of traveling waves to the Keller-Segel model. The results are proved via the phase portrait analysis and the (weighted) energy estimates under a change of variable. In the talk, the background of the model will be introduced and the main challenges and primary ideas of the proved results will be sketched. The numerical simulations will be shown and the remaining open problems will also be presented. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 33 Asymptotic Behavior of Solutions for Degenerate Fisher Type Equations Yaping Wu Capital Normal University,China [email protected] Consider the degenerate Fisher equation in one dimensional space or in a cylinder R , with bounded , (1) It is well known that in one dimensional space there exists a minimal speed such that (1) has a traveling front solution satisfying and if and only if ; and the wave front with the minimal speed decay exponentially at and is globally exponentially stable in exponentially weighted spaces, while the waves with noncritical speeds decay algebraically at and is locally stable in some algebraically weighted spaces. In this talk we shall be more interested in the existence of generalized traveling waves and the asymptotic behavior of solutions of (1) in one dimensional space with more general initial values decaying non‐exponentially in space. Our results show that for more general slowly decaying initial value the solution still moves like a wave front and the decaying rate of initial value uniquely determines the asymptotic speed of the level set of the solution. In this talk we shall also talk about our recent progress on the existence and stability of cylinder waves of (1) in higher dimensional space when It’s a joint work with Yanxia Wu and Junfeng He. ---------------------------------------------------------------------------------------------------------------------Some Studies on the Well-posedness Theories of the Prandtl Layer Equations Tong Yang City University of Hong Kong, China [email protected] In this talk, we will present some recent joint works with Chengjie Liu and YaguangWang on the well-posedness theories of the Prandtl layer equations. Firstly, the Prandtl equations in three space variables are studied both locally and globally in time under some constraint on its flow structure. It reveals that the classical Burgers equation plays an important role in the analysis. And the monotonicity condition on the velocity and the favorable condition on pressure are illustrated in the 3D setting. Further, the linear stability of this structured flow is justified. Finally, we will present some related study on the compressible flow. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 34 Global Solutions of Multi-dimensional Inhomogeneous Scalar Conservation Law. Xiaozhou Yang Institute of Physics and Mathematics, Wuhan, Academy of China [email protected] In this talk, we will present the non-selfsimilar Riemman solutions of multi-dimensional inhomogeneous scalar conservation law, and we will show some new structures. ---------------------------------------------------------------------------------------------------------------------Global Existence of Radial Solutions for Semilinear Hyperbolic Systems in 3D Silu Yin Fudan University, China [email protected] In this talk we will give a proof of global existence of radial solutions for general semilinear hyperbolic systems in 3D with small 2,1 3 ( ) W R data. We reduce the three dimensional general hyperbolic system to a new system under rotational invariance, and obtain a bilinear estimate which is also effective to hyperbolic systems with zero eigenvalues. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 35 Newtonian Limit of Maxwell Fluid Flows Wen-An Yong Tsinghua University, China [email protected] In this work, we revise the classical Maxwell's constitutive relation and formulate a system of first-order partial differential equations with two parameters for compressible viscoelastic fluid flows. The system is shown to possess a nice conservation-dissipation (relaxation) structure and therefore is symmetrizable hyperbolic. Moreover, for smooth flows we rigorously verify that the revised Maxwell's constitutive relations are compatible with Newton's law of viscosity. ---------------------------------------------------------------------------------------------------------------------The Spectrum Analysis of Some Kinetic Equations Hongjun Yu South China Normal University, China [email protected] In this talk, we discuss about spectrum analysis of some kinetic equations, including Boltzmann equation without non-cut-off hard potentials and the Landau equation with г≥ -2. This is joint work with Prof. Tong Yang. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 36 Transonic Shocks in Steady Compressible Euler Flows Hairong Yuan East China Normal University, China [email protected] I will introduce the physical phenomena of transonic shocks, and review the progresses on the mathematical studies of related boundary value problems of the steady compressible Euler equations. The talk is based upon joint works with many collaborators. ---------------------------------------------------------------------------------------------------------------------Global Wellposedness for the Incompressible Fluids System with Some Class of Large Initial Velocity Ting Zhang Zhejiang University, China [email protected] In this talk, we consider the following 3-D incompressible inhomogeneous Navier-Stokes equations with initial data in the critical Besov spaces. Using the incompressible condition and the nonlinear structure, we obtain the existence and uniqueness of the global solution with large initial vertical velocity component. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 37 The Vlasov-Poisson-Boltzmann System near Maxwellians in the Whole Space Huijiang Zhao Wuhan University, China [email protected] This talk is concerned with some recent progress on the construction of global smooth solutions to the one-species Vlasov-Poisson-Boltzmann system near Maxwellians in the whole space for the whole range of cutoff intermolecular ---------------------------------------------------------------------------------------------------------------------No-Blow-Up of Solutions to a Nonlinear System of Variational Wave Systems Yuxi Zheng The Penn State University, USA [email protected] We consider a hyperbolic wave system that models nematic liquid crystals in which the twisting coefficient dominate the other two coefficients of bending and splaying. If the bending and splaying coefficients are assumed to be equal, then the system remains nonlinear but we show that the solutions will remain smooth for smooth initial data. The context of this interesting result will be shown to be mostly blow-up type of solutions. This is a joint result with Jingchi Huang. 2014 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 38 Spectrum Analysis of the Vlasov-Poisson-Boltzmann System Mingying Zhong Guangxi University/The City University of Hong Kong, China [email protected] By identifying a norm capturing the effect of the forcing governed by the Poisson equation, we give a detailed spectrum analysis on the linearized Vlasov-Poisson-Boltzmann system around a global Maxwellian. It is shown that the electric field governed by the self-consistent Poisson equation plays a key role in the analysis so that the spectrum structure is genuinely different from the well-known one of the Boltzmann equation. Based on this, we give the optimal time decay rates of solutions to the equilibrium. ---------------------------------------------------------------------------------------------------------------------A New Proof of Global Existence of Entropy Weak Solutions for Systems of Conservation Laws Yi Zhou Fudan University, China [email protected] In this talk, we will give a new and simple proof of the classical theorem of Glimmm that systems of conservation laws in one space dimension which are strictly hyperbolic and genuinely nonlinear admits a global entrpy weak solution for small BV data. We approximate n\times n systems of conservation law on any time interval [0,T] by an artificially choosing 2n\times 2n systems of quasilinear hyperbolic equations which has a smooth solution on [0,T] and converges to the entropy weak solution of the original hyperbolic conservation laws.