Limites hydrodynamiques
Limites hydrodynamiques de l'équation de Boltzmann
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 degeneracy and shock waves.
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.
Linear independence of boundary traces of eigenfunctions of elliptic and Stokes operators and applications
This paper is divided into two parts and focuses on the linear independence of boundary traces of eigenfunctions of boundary value problems. Part I deals with second-order elliptic operators, and Part II with Stokes (and Oseen) operators. Part I: Let be an eigenvalue of a second-order elliptic operator defined on an open, sufficiently smooth, bounded domain Ω in ℝⁿ, with Neumann homogeneous boundary conditions on Γ = tial Ω. Let be the corresponding linearly independent (normalized) eigenfunctions...
Linear instability implies nonlinear instability for various types of viscous boundary layers
Linear response of the gate system for protection of the Venice Lagoon. Note I: Transverse free modes
The free oscillations of the gate system proposed [1,2] to defend the Venice Lagoon from the phenomenon of high water are analyzed. Free transverse modes of oscillations exist which may be either subharmonic or synchronous with respect to typical waves in the Adriatic sea. This result points out the need to examine whether such modes may be excited as a result of a Mathieu type resonance occurring when the gate system is forced by incident waves. The latter investigation is performed in part 2 of...
Linear response of the gate system for protection of the Venice Lagoon. Note II: Excitation of transverse suhharmonic modes
We show that the transverse subharmonic modes characterizing the free oscillations of the gate system proposed to defend the Venice Lagoon from the phenomenon of high water (see Note I[1]) can be excited when the gate system is forced by plane monochromatic waves orthogonal to the gates with the typical characteristics of large amplitude waves in the Adriatic sea close to the lagoon inlets. A linear stability analysis of the coupled motion of the system sea-gates-lagoon reveals that for typical...
Linear stability results in a magnetothermoconvection problem.
Linearization and normal form of the Navier-Stokes equations with potential forces
Linear-quadratic optimal control for the Oseen equations with stabilized finite elements
For robust discretizations of the Navier-Stokes equations with small viscosity, standard Galerkin schemes have to be augmented by stabilization terms due to the indefinite convective terms and due to a possible lost of a discrete inf-sup condition. For optimal control problems for fluids such stabilization have in general an undesired effect in the sense that optimization and discretization do not commute. This is the case for the combination of streamline upwind Petrov-Galerkin (SUPG) and pressure...
Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations
Liquid Drops in a Viscous Fluid under the Influence of Gravity and Surface Tension.
Local a posteriori estimates for the Stokes problem.
Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations
We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.
Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations
We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.