Invariant measures for a nonlinear Schrödinger equation

Benedetta Ferrario (U Pavia)

Feb 13. 2024, 09:45 — 10:25

We consider a  Schrödinger equation with  defocusing polynomial nonlinearity and multiplicative noise.

In a bounded 2D domain, by considering Dirichlet boundary conditions we prove the existence of an invariant measure; uniqueness holds for a particular choice of the noise. Similar results hold for Neumann b.c. as well or in a bounded manifold without boundary. The technique is based on the Krylov-Bogoliubov  technique in the setting of weakly topologies. This is based on a joint work with Z. Brzezniak and M. Zanella.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Stochastic Partial Differential Equations (Workshop)
Organizer(s):
Sandra Cerrai (U of Maryland)
Martin Hairer (Imperial College London)
Carlo Marinelli (University College London)
Eulalia Nualart (U Barcelona)
Luca Scarpa (Politecnico Milano)
Ulisse Stefanelli (U of Vienna)