Random data Cauchy problem for supercritical Schrödinger equations
Recent progress on the blow-up problem of Zakharov equations
Recent Results on the Cauchy Problem for Focusing and Defocusing Gross-Pitaevskii Hierarchies
In this paper, we review some of our recent results in the study of the dynamics of interacting Bose gases in the Gross-Pitaevskii (GP) limit. Our investigations focus on the well-posedness of the associated Cauchy problem for the infinite particle system described by the GP hierarchy.
Reductions of multicomponent mKdV equations on symmetric spaces of DIII-type.
Regularity bounds on Zakharov system evolutions.
Remarks on global existence and compactness for solutions in the critical nonlinear schrödinger equation in 2D
In the talk we shall present some recent results obtained with F. Merle about compactness of blow up solutions of the critical nonlinear Schrödinger equation for initial data in . They are based on and are complementary to some previous work of J. Bourgain about the concentration of the solution when it approaches to the blow up time.
Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
We concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound from below the blow-up rate for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than , the expected one. Moreover, we state that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.
Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.
Remarques sur l'analyse semi-classique de l'équation de Schrödinger non linéaire
Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems.
Rôle des oscillations quadratiques dans des équations de Schrödinger non linéaire