In this talk we address the issue of existence of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the convergence, as the viscosity goes to zero, of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions...

We use the bivariate spline method to solve the time evolution Navier-Stokes equations numerically. The bivariate spline we use in this paper is the spline space of smoothness r and degree 3r over triangulated quadrangulations. The stream function formulation for the Navier-Stokes equations is employed. Galerkin's method is applied to discretize the space variables of the nonlinear fourth order...

This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of ...

The present work introduces a modified scheme for the solution of compressible 2-D full Navier-Stokes equations, using Flux Vector Splitting method. As a result of this modification, numerical diffusion is reduced. The computer code which is developed based on this algorithm can be used easily and accurately to analyze complex flow fields with discontinuity in properties, in cases such as shock...

The standard discretization of the Stokes and Navier-Stokes équations in vorticity and stream function formulation by affine finite éléments is known for its bad convergence. We present here a modified discretization, we prove that the convergence is improved and we establish a priori error estimâtes. Résumé. Il est bien connu que la discrétisation usuelle des équations de Stokes et de Navier-S...

The present work introduces a modified scheme for the solution of compressible 2-D full Navier-Stokes equations, using Flux Vector Splitting method. As a result of this modification, numerical diffusion is reduced. The computer code which is developed based on this algorithm can be used easily and accurately to analyze complex flow fields with discontinuity in properties, in cases such as shock...

The problem considered is the Stokes and Navier-Stokes flow through a system of two pipes in the gravity field; inside a vertical pipe there is a free heavy piston. Theoretical analysis, the existence and non-uniqueness of solution, has been completed recently by the authors. Here we present numerical analysis, using finite elements methods, of the stationary state with respect to the angle bet...

In [4] the authors consider the two dimensional Navier-Stokes equations in the exterior of an obstacle shrinking to a point and determine the limit velocity. Here we consider the same problem in the three dimensional case, proving that the limit velocity is a solution of the Navier-Stokes equations in the full space.

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.