We recover the Navier-Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a meso-scopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier-Stokes equation in a fixed time interval. The proof does not use non-gradient methods or the multi-scale analysis due to the long range jumps.

are called stationary Stokes equations, where u : Ω→ R denotes the velocity of the uid, p : Ω→ R denotes the pressure and f : Ω → R is the density of forces acting on the uid (e.g. gravitational force). The Stokes equations govern a ow of a steady, viscous, incompresible uid. We note that (1) is called the momentum equation and (2) is called the incompressibility equation. We supplement the sys...

A small parameter technique is used to derive Reynolds' lubrication equation from the Stokes equation. The error associated with the approximation is estimated in suitable norms.

This note presents the results from “Ergodicity of the degenerate stochastic 2D Navier-Stokes equation” by M. Hairer and J. C. Mattingly. We study the Navier-Stokes equation on the two-dimensional torus when forced by a finite-dimensional Gaussian white noise and give conditions under which the system is ergodic. In particular, our results hold for specific choices of four-dimensional Gaussian ...

In this paper, we study the dynamics of a two-dimensional stochastic Navier-Stokes equation on a smooth domain, driven by multiplicative white noise. We show that solutions of the 2D Navier-Stokes equation generate a perfect and locally compacting C1,1 cocycle. Using multiplicative ergodic theory techniques, we establish the existence of a discrete non-random Lyapunov spectrum for the cocycle. ...

The incompressible Navier-Stokes equations are discretized in space and integrated in time by the method of lines and a semi-implicit method. In each time step a set of systems of linear equations has to be solved. The size of the time steps are restricted by stability and accuracy of the time-stepping scheme, and convergence of the iterative methods for the solution of the systems of equations...

The Stokes equations are the linearization of the incompressible Navier-Stokes equations about zero. They may be derived directly from the Boltzmann equation as the formal limit of moment equations for an appropriately scaled family of Boltzmann solutions. The present paper establishes this limit for the Boltzmann equation considered over a periodic spatial domain for bounded collision kernels....

A general procedure to obtain analytic solutions of the linearized lattice Boltzmann equation for simple ows is developed. As examples, the solutions for the Poiseuille and the plane Couette ows in two-dimensional space are obtained and studied in detail. The solutions not only have a component which is the solution of the Navier-Stokes equation, they also include a kinetic component which cann...

The paper deals with the homogenization of rigid heterogeneous plates. Assuming that the coefficients are equi-bounded in L1, we prove that the limit of a sequence of plate equations remains a plate equation which involves a strongly local linear operator acting on the second gradients. This compactness result is based on a div-curl lemma for fourthorder equations. On the other hand, using an i...

Most researches on fluid dynamics are mostly dedicated to obtain the solutions of Navier-Stokes equation which governs fluid flow with particular boundary conditions and approximations. We propose an alternative approach to deal with fluid dynamics using the lagrangian. We attempt to develop a gauge invariant lagrangian which reconstructs the Navier-Stokes equation through the Euler-Lagrange eq...