-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle.
-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle
L2 Decay for the Navier-Stokes Flow in Halfspaces.
La vitesse de propagation dans le problème de la digue
Lagrangian approximations and weak solutions of the Navier-Stokes equations
The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid....
L’élément -bulle/
Letter to the editor.
Limit of models of compressible fluids. (Limite de modèles de fluides compressibles.)
Limites réversibles et irréversibles de systèmes de particules.
Il s’agit de comparer les différents résultats et théorèmes concernant dans un cadre essentiellement déterministe des systèmes de particules. Cela conduit à étudier la notion de hiérarchies d’équations et à comparer les modèles non linéaires et linéaires. Dans ce dernier cas on met en évidence le rôle de l’aléatoire. Ce texte réfère à une série de travaux en collaboration avec F. Golse, A. Gottlieb, D. Levermore et N. Mauser.
Limiting behavior for an iterated viscosity
Limiting Behavior for an Iterated Viscosity
The behavior of an ordinary differential equation for the low wave number velocity mode is analyzed. This equation was derived in [5] by an iterative process on the two-dimensional Navier-Stokes equations (NSE). It resembles the NSE in form, except that the kinematic viscosity is replaced by an iterated viscosity which is a partial sum, dependent on the low-mode velocity. The convergence of this sum as the number of iterations is taken to be arbitrarily large is explored. This leads to a limiting...
Linear flow in porous media with double periodicity.
Linear flow problems in 2D exterior domains for 2D incompressible fluid flows
The paper analyzes the issue of existence of solutions to linear problems in two dimensional exterior domains, linearizations of the Navier-Stokes equations. The systems are studied with a slip boundary condition. The main results prove the existence of distributional solutions for arbitrary data.
Linearization and normal form of the Navier-Stokes equations with potential forces
Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations
Local and global existence and behaviour for of solutions of the Navier-Stokes equations
Local error estimates for finite element discretization of the Stokes equations
Local exact controllability for the -d compressible Navier-Stokes equations
In this talk, I will present a recent result obtained in [6] with O. Glass, S. Guerrero and J.-P. Puel on the local exact controllability of the -d compressible Navier-Stokes equations. The goal of these notes is to give an informal presentation of this article and we refer the reader to it for extensive details.
Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions
In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T>0. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.
Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids
Local existence of solutions is proved for equations describing the motion of a viscous compressible barotropic and self-gravitating fluid in a domain bounded by a free surface. First by the Galerkin method and regularization techniques the existence of solutions of the linearized momentum equations is proved, next by the method of successive approximations local existence to the nonlinear problem is shown.