Palestrante: Simão Correia (Universidade de Lisboa)

Data: 03/11/2016 (excepcionalmente, a palestra dessa semana será na 5a feira)
Hora: 13:30 h
Local: C-119

Título: Spatial plane waves for the NLS: local existence and stability results

Resumo: In this talk, we shall consider classes of particular solutions for the nonlinear Schrödinger equation. The simplest case appears when one requires that the solution must also satisfy a transport equation in the spatial variables. These solutions are not contained in the known local well-posedness theories. We show local well-posedness on functional spaces which include these solutions and prove their stability with respect to localized perturbations. To this end, we consider a new functional transform, the plane wave transform, which has some quite unexpected properties and generalizes Fourier and Laplace's transform. A comment on further applications to other PDE's shall be made. This is a joint work with Mário Figueira.