On the Nonlinear Schroedinger Equations with multiplicative white noise

by Prof. Nicola Visciglia (University of Pisa)

Thursday 9 Feb 2023, 15:00 → 16:00 Europe/Rome

Ex-ISEF/Building-Main Lecture Hall (GSSI)

We consider NLS with a multiplicative white noise on T^2 and we study the existence and uniqueness of global solutions. The topic is at the interface between dispersive PDEs and probability, along the seminar we shall give an overview of the main techniques involved in our analysis. In particular we shall discuss on one hand the renormalization procedure that allows to define the probabilistic product of distributions at negative regularity, on the other hand we shall discuss the deterministic Strichartz estimates on T^2. As we shall see the main difficulty is due to the low regularity of the white noise potential that does not allow to apply directly the techniques useful in the analysis of the classical NLS with a smooth and deterministic potential.