The purpose of this paper is to introduce a viscosity approximation forward-backward splitting method for the implicit midpoint rule of an accretive operators and m-accretive operators in Banach spaces. The strong convergence of this viscosity method is proved under certain assumptions imposed on the sequence of parameters. The results presented in the paper extend and improve some recent resul...

Laminar free convection flow of viscous, incompressible fluid with variable viscosity and viscous dissipation through two horizontal parallel walls embedded in a porous medium is studied. Arrhenius model is used in which the variable viscosity is used to be decreasing exponentially with temperature. An approximation technique is defined to obtain the solution of the coupled non-linear equations...

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations with degenerate viscosity, and a nonlinear third-order differential operator, with the quantum Bohm potential, and the damping terms. The global weak solution...

An a priori derivation of the lattice Boltzmann equations for binary mixtures is provided by discretizing the Boltzmann equations that govern the evolution of binary mixtures. The present model leads to a set of two-fluid hydrodynamic equations for the mixture. In existing models, employing the single-relaxation-time approximation, the viscosity and diffusion coefficients are coupled through th...

We show that first approximations to the bulk viscosity ηv are expressible in terms of factors that depend on the sound speed vs, the enthalpy, and the interaction (elastic and inelastic) cross section. The explicit dependence of ηv on the factor ( 1 3 − v 2 s ) is demonstrated in the ChapmanEnskog approximation as well as the variational and relaxation time approaches. The interesting feature ...

X iv :0 90 8. 30 57 v1 [ m at h. A P] 2 1 A ug 2 00 9 EXISTENCE AND REGULARITY FOR THE GENERALIZED MEAN CURVATURE FLOW EQUATIONS RONGLI HUANG AND JIGUANG BAO Abstract. By making use of the approximation method, we obtain the existence and regularity of the viscosity solutions for the generalized mean curvature flow. The asymptotic behavior of the flow is also considered. In particular, the Diri...

It has been suggested that for fluids in which the rate of strain varies appreciably over length scales of the order of the intermolecular interaction range, the viscosity must be treated as a nonlocal property of the fluid. The shear stress can then be postulated to be a convolution of this nonlocal viscosity kernel with the strain rate over all space. In this Letter, we confirm that this post...

We follow the diffusive motion of colloidal particles of diameter d in soap films of varying thickness h with fluorescence microscopy. Diffusion constants are obtained both from one- and two-particle microrheological measurements of particle motion in these films. These diffusion constants are related to the surface viscosity of the interfaces comprising the soap films, by means of the Trapezni...

Two viscous stabilization methods, namely the spectral vanishing viscosity (SVV) technique and the entropy viscosity method (EVM), are applied to flows of interest in geophysics. First, following a study restricted to one space dimension [17], the spectral element approximation of the shallow water equations is stabilized using the EVM. Our recent advances are here carefully described. Second, ...

This paper considers an extension of the Merton optimal investment problem to the case where the risky asset is subject to transaction costs and capital gains taxes. We derive the dynamic programming equation in the sense of constrained viscosity solutions. We next introduce a family of functions (Vε)ε>0, which converges to our value function uniformly on compact subsets, and which is character...