Some new local and global well-posedness results for the nonlinear Schrödinger equation

Jeudi 11 janvier 2018 15:45-16:45 - Simão Correia - Université de Strasbourg

Résumé : In this presentation, we shall consider the nonlinear Schrödinger equation on $\mathbbR^d$,

$$iu_t + \Delta u + \lambda |u|^\sigma u = 0$$

with an initial condition at $t=0$. This is already a classical equation, with a vast literature regarding the behaviour of the solutions to this problem. We discuss the extension of the $H^1$ local well-posedness theory to some larger spaces which, in particular, do not lie inside $L^2$. As a byproduct, we develop the theory for the plane wave transform, which is of independent mathematical interest. If time allows, we present some global existence results, which either rely on a small data theory or on the concept of finite speed of disturbance.

Lieu : IMO, Salle 3L8

Some new local and global well-posedness results for the nonlinear Schrödinger equation  Version PDF