Nader Masmoudi

Incompressible limit for a viscous compressible fluid

Abstract We prove various asymptotic results concerning global (weak) solutions of compressible isentropic Navier-Stokes equations. More precisely, we show various results establishing the convergence, as the density becomes constant and the Mach number goes to 0, towards solutions of incompressible models (Navier-Stokes or Euler equations). Most of these results are global in time and without size restriction on the initial data. We also observe rigorously the linearized system around constant flows.

Incompressible, inviscid limit of the compressible Navier–Stokes system

Abstract We prove some asymptotic results concerning global (weak) solutions of compressible isentropic Navier–Stokes equations. More precisely, we establish the convergence towards solutions of incompressible Euler equations, as the density becomes constant, the Mach number goes to 0 and the Reynolds number goes to infinity.

Chapter 3 – Examples of Singular Limits in Hydrodynamics

Abstract This chapter is devoted to the study of some asymptotic problems in hydrodynamics. In particular, we will review results about the inviscid limit, the compressible–incompressible limit, the study of rotating fluids at high frequency, the hydrodynamic limit of the Boltzmann equation as well as some homogenization problems in fluid mechanics.

Une approche locale de la limite incompressible

Resume Nous etablissons dans cette Note un resultat local de convergence faible des solutions des equations de Navier-Stokes compressibles, quand le nombre de Mach tend vers 0, vers une solution a la Leray des equations de Navier-Stokes incompressibles.

Uniform Regularity for the Navier–Stokes Equation with Navier Boundary Condition

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier–Stokes equation with the Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in L∞. This allows us to obtain the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.

Global Well-Posedness for a Smoluchowski Equation Coupled with Navier-Stokes Equations in 2D

We prove global existence for a nonlinear Smoluchowski equation (a nonlinear Fokker-Planck equation) coupled with Navier-Stokes equations in 2d. The proof uses a deteriorating regularity estimate in the spirit of [5] (see also [1]).

From vlasov-Poisson system to the incompressible Euler system

This paper is devoted to the proof of the convergence of the Vlasov-Poisson system to the incompressible Euler equations in the so-called quasi-neutral regime for cold electrons. The convergence is global in time and for general initial data as long as a strong solution for the Euler system is known to exist. This investigation extends the results of Y. Brenier [1] where the case of “well-prepared” initial data was handled.

FROM THE KLEIN–GORDON–ZAKHAROV SYSTEM TO THE NONLINEAR SCHRÖDINGER EQUATION

In this paper, we study the convergence of solutions in the limit from the Klein–Gordon–Zakharov system to the nonlinear Schrodinger equation. The major difficulties are resonant bilinear interactions whose frequency are going to infinity, and the diverging total energy. We overcome them by combining bilinear estimates for non-resonant interactions and a modified nonlinear energy at the resonant frequency.

Homogenization in polygonal domains

We consider the homogenization of elliptic systems with \eps-periodic coefficients. Classical two-scale approximation yields a O(\eps) error inside the domain. We discuss here the existence of higher order corrections, in the case of general polygonal domains. The corrector depends in a non-trivial way on the boundary. Our analysis extends substantially previous results obtained for polygonal domains with sides of rational slopes.

Landau Damping: Paraproducts and Gevrey Regularity

We give a new, simpler, but also and most importantly more general and robust, proof of nonlinear Landau damping on