A nonlinear Schrödinger equation with fractional noise

Date/heure
6 novembre 2020
11:00 - 12:00

Oratrice ou orateur
Nicolas Schaeffer

Catégorie d'évènement
Séminaire EDP, Analyse et Applications (Metz)


Résumé

The aim of this talk is to study a stochastic Schrödinger equation with a quadratic nonlinearity and a space-time fractional perturbation, in space dimension $dleq 3$. When the Hurst index is large enough, we will prove local well-posedness of the problem using classical arguments. I will briefly talk about the case where we deal with a small Hurst index since even the interpretation of the equation needs some care. A renormalization procedure must come into the picture, leading to a Wick-type interpretation of the model. Our fixed-point argument then involves some specific regularization properties of the Schrödinger group, which allows us to cope with the strong irregularity of the solution. This is a joint work with Aurélien Deya and Laurent Thomann.