Taoufik Hmidi

Global Well-Posedness for Euler–Boussinesq System with Critical Dissipation

In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.

Blowup theory for the critical nonlinear Schrödinger equations revisited

In this note we prove a refined version of compactness lemma adapted to the blowup analysis and we use it to give direct and simple proofs to some classical results of blowup theory for critical nonlinear Schrodinger equations (mass concentration, classification of the singular solutions with minimal mass...).

On the Global Well-Posedness of the Critical Quasi-Geostrophic Equation

We prove the global well-posedness of the critical dissipative quasi-geostrophic equation for large initial data belonging to the critical Besov space

On the global well-posedness of the Euler–Boussinesq system with fractional dissipation

\dot B^0_{\infty,1}(\RR^2).

Boundary Regularity of Rotating Vortex Patches

Abstract We study the global well-posedness of the Euler–Boussinesq system with the term dissipation | D | α on the temperature equation. We prove that for α > 1 the coupled system has a global unique solution for initial data with critical regularities.

Remarks on the blowup for the L-2-critical nonlinear Schrodinger equations

In this paper we prove the global well-posedness for a three-dimensional Boussinesq system with axisymmetric initial data. This system couples the Navier-Stokes equation with a transport-diffusion equation governing the temperature. Our result holds uniformly with respect to the heat conductivity coefficient

On the V-states for the Generalized Quasi-Geostrophic Equations

\kappa \geq 0

Doubly Connected

which may vanish.

V

We show that the boundary of a rotating vortex patch (or V-state, in the terminology of Deem and Zabusky) is C∞, provided the patch is close to the bifurcation circle in the Lipschitz norm. The rotating patch is also convex if it is close to the bifurcation circle in the C2 norm. Our proof is based on Burbea’s approach to V-states.