In this paper we consider the three–dimensional Navier–Stokes equations subject to periodic boundary conditions or in the whole space. We provide sufficient conditions, in terms of one direction derivative of the velocity field, namely, uz , for the regularity of strong solutions to the three-dimensional Navier–Stokes equations.

The improved Boussinesq equation is studied in this paper. Control properties for this equation posed on a bounded interval are first considered. When the control acts through the Dirichlet boundary condition the linearized system is proved to be approximately but not spectrally controllable. In a second part, the equation is posed on the one-dimensional torus and distributed moving controls ar...

We study a discrete spatial model for invasive allele spread in which two alleles compete preemptively, initially only the " residents " (weaker competitors) being present. We find that the spread of the advantageous mutation is well described by homogeneous nucleation; in particular, in large systems the time-dependent global density of the resident allele is well approximated by Avrami's law....

We study convergence to equilibrium for certain spatially inhomogenous kinetic equations, such as discrete velocity models or a linearization of a kinetic model for cometary flow. For such equations, the convergence to a unique equilibrium state is the result of, firstly, the dissipative effects of the collision operator, which morphs the solution towards an entropy minimizing local equilibrium...

The system −divS(D(u)) + (u · ∇)u +∇π = f , divu = 0, is considered on a bounded three-dimensional domain under no–stick boundary value conditions, where S has p-structure for some p < 2 and D(u) is the symmetrized gradient of u. Various regularity results for the velocity u and the pressure π in fractional order Sobolev and Nikolskii spaces are obtained.

On the micro- and nanoscale, classical hydrodynamic boundary conditions such as the no-slip condition no longer apply. Instead, the flow profiles exhibit "slip" at the surface, which is characterized by a finite slip length (partial slip). We present a new, systematic way of implementing partial-slip boundary conditions with arbitrary slip length in coarse-grained computer simulations. The main...

As the number of applications of micro electro mechanical systems, or MEMS, increase, the variety of flow geometries that must be analyzed at the micro-scale is also increasing. To date, most of the work on MEMS scale fluid mechanics has focused on internal flow geometries, such as microchannels. As applications such as micro-scale flyers are considered, it is becoming necessary to consider ext...

We consider the initial-boundary value problem of two-dimensional inviscid heat conductive Boussinesq equations with nonlinear heat diffusion over a bounded domain with smooth boundary. Under slip boundary condition of velocity and the homogeneous Dirichlet boundary condition for temperature, we show that there exists a unique global smooth solution to the initial-boundary value problem for H i...

An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the viscous-slip and the half-space thermal-creep problems for a binary gas mixture. The kinetic equations used to describe the flow are based on the McCormack model for mixtures. In addition to a computation of the viscous-slip and thermal-slip coefficient...