We consider the Navier-Stokes-Alpha model as an approximation of turbulent flows under realistic, non-periodic, boundary conditions. We derive that the variational formulation of Navier-Stokes-Alpha model under non-periodic boundary conditions, and prove that it has a unique weak solution. Next we consider finite element approximation of the model. We give semi discretization of the model and p...

The paper is devoted to the analysis of a hydrodynamic limit for the Vlasov-Navier-Stokes equations.This system is intended to model the evolution of particles interacting with a fluid. The coupling arises from the force terms. The limit problem is the Navier-Stokes system with non constant density. The density which is involved in this system is the sum of the (constant) density of the fluid a...

This article is devoted to the study of the nonhomogeneous incompressible Navier-Stokes equations in space dimension three. By making use of the “weakly nonlinear” energy estimate approach introduced by Lei and Zhou in [16], we establish two logarithmically improved blow-up criteria of the strong or smooth solutions subject to vacuum for the 3D nonhomogeneous incompressible Navier-Stokes equati...

A mixed finite element method for the Navier–Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier–Stokes equations and the classical theory extends naturally to this setting. Finite element spaces satisfying the associated inf–sup conditions are developed. Mathematics Subject Classification. 65N60,...

Abstract. In this paper, we study the regularities of solutions of nonlinear stochastic partial differential equations in the framework of Hilbert scales. Then we apply our general result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau’s equations on the real line, stochastic 2D Navier-Stokes equations in the whole space and a stochastic tamed 3D Navier-Stokes ...

In this paper, we present a new pressure-correction projection scheme for solving the time-dependent Navier-Stokes equations, which is based on the Crank-Nicolson extrapolation method in the time discretization. Error estimates for the velocity and the pressure of semidiscretized scheme are derived by interpreting the projection scheme as second-order time discretization of a perturbed system w...

We consider stationary solutions of the incompressible Navier-Stokes equations for an exterior domain in two dimensions. We prove that asymptotically in the down–stream direction, the leading order deviation from the constant flow is universal, i.e. independent of the details of the domain. To get this result, we show that the (elliptic) Navier–Stokes equations can be interpreted as a dynamical...

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...

Abstract. The procedure of solving the system of the Navier-Stokes equations is proposed. The initial conditions: the velocity divergence (dilatation) being zero and the temperature being the known function, the initial density being constant. The problem is set in the infinite space. The solution of the Navier-Stokes equations was reduced to the solution of integral equations of the Volterra t...