Lie symmetries analysis of the shallow water equations.
Lie-group analysis of radiative and magnetic field effects on free convection and mass transfer flow past a semi-infinite vertical flat plate.
Limite incompressible de solutions du système d’Euler compressible 2-D dans certains cas mal préparés
Les effets dispersifs permettent de passer à la limite dans le système d’Euler compressible 2-D isentropique, quand le nombre de Mach tend vers zéro, même si les données initiales ne sont pas uniformément régulières.Ceci mène à des résultats de convergence vers des solutions non régulières du système d’Euler incompressible, comme les poches de tourbillon ou les solutions de Yudovich.
Limite quasi-neutre en dimension
L’objet de cette note est d’étudier la limite quasineutre des équations de Vlasov Poisson en dimension d’espace. Ceci inclut l’obtention de résultats d’existence pour le système limite ainsi que la preuve de la convergence.
Limites hydrodynamiques de l'équation de Boltzmann
Liouville integrability of geometric variational problems.
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.
Local exact lagrangian controllability of the Burgers viscous equation
Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids
The local existence and the uniqueness of solutions for equations describing the motion of viscous compressible heat-conducting fluids in a domain bounded by a free surface is proved. First, we prove the existence of solutions of some auxiliary problems by the Galerkin method and by regularization techniques. Next, we use the method of successive approximations to prove the local existence for the main problem.
Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid
Local existence of solutions is proved for equations describing the motion of a magnetohydrodynamic incompressible fluid in a domain bounded by a free surface. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linarized equations is proved; next by the method of successive aproximations the local existence is shown for the nonlinear problem....
Local smooth solution and non-relativistic limit of radiation hydrodynamics equations.
Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods
We demonstrate that there exist no self-similar solutions of the incompressible magnetohydrodynamics (MHD) equations in the space . This is a consequence of proving the local smoothness of weak solutions via blowup methods for weak solutions which are locally . We present the extension of the Escauriaza-Seregin-Sverak method to MHD systems.
Local well-posedness for a two-phase model with magnetic field and vacuum
This paper proves the local well-posedness of strong solutions to a two-phase model with magnetic field and vacuum in a bounded domain without the standard compatibility conditions.
Local well-posedness for the incompressible Euler equations in the critical Besov spaces
In this paper we establish the existence and uniqueness of the local solutions to the incompressible Euler equations in , , with any given initial data belonging to the critical Besov spaces . Moreover, a blowup criterion is given in terms of the vorticity field....
Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces
We study local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation for the initial data u₀(x) in the Besov space with max(3/2,1 + 1/p) < s ≤ m and (p,r) ∈ [1,∞]², where g:ℝ → ℝ is a given -function (m ≥ 4) with g(0)=g’(0)=0, and κ ≥ 0 and γ ∈ ℝ are fixed constants. Using estimates for the transport equation in the framework of Besov spaces, compactness arguments and Littlewood-Paley theory, we get a local well-posedness result.
Logarithmically improved regularity criteria for the micropolar fluid equations
We discuss the 3D incompressible micropolar fluid equations, and give logarithmically improved regularity criteria in terms of both the velocity field and the pressure in Morrey-Campanato spaces, BMO spaces and Besov spaces.
Long-time asymptotics for the damped Boussinesq equation in a disk.
Long-time asymptotics of solutions for the second initial-boundary value problem for the damped Boussinesq equation.