GdT Scattering des EDP non-lineaires

Scattering theory for Schrodinger equations (Giorgio Velo)

Basic ideas in scattering theory will be introduced and applied to the nonlinear Schroedinger equation (NLS) and to the Hartree equation (HE). In situations of short range the Cauchy problem with infinite initial time will be presented and asymptotic completeness will be discussed. The boundary between short and long range will be illustrated in detail. Some general information on the Cauchy problem with infinite initial time for the long range HE will be given.

Cours 1

• Introduction au "Scattering" des equations de Schroedinger non-lineaires; inegalites de Strichartz.

Cours 2

• Problemes de Cauchy avec donnees initiales a l'infini: $$L^{2}(\mathbb{R}^{n})$$, $$H^{1}(\mathbb{R}^{n})$$.

Cours 3

• Problemes de Cauchy en $$Y^{1}(I)$$ ; loi de transformation pseudoconformes; completude asymptotique.