In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 − P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtain...

This work will be the first chapter of a book in progress. This project aims to study the 3D periodic Navier-Stokes equations, existence and regularity up-date results. We also shall study some LES related models like Leray-alpha, Bardina, ADM and deconvolution models, including the most recent results on these models. We have take care in this work to make rigorous the mathematical foundations...

We consider the convergence in the L norm, uniformly in time, of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions. We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow, and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer, then the inviscid limit holds. M...

A class of sufficient conditions of local regularity for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations are discussed. The corresponding results are formulated in terms of functionals which are invariant with respect to the Navier-Stokes equations scaling. The famous Caffarelli-Kohn-Nirenberg condition is contained in that class as a particular case. 1991...