Local and almost global solutions for quasi-linear Schrödinger equations on tori

Nom de l'orateur
Roberto Feola
Etablissement de l'orateur
Université de Nantes
Date et heure de l'exposé
Lieu de l'exposé
Salle des séminaires

We consider a class of quasi-linear, Hamiltonian Schrödinger equations on the d dimensional torus. We discuss the problem of existence and unicity of classical solutions of the Cauchy problem associated to the equation with initial conditions in the Sobolev space H^s, with s large. We also present results about the lifespan and stability of small solutions. The proofs of such results involves techniques of para-differential calculus combined with normal form theory.