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
ESI Boltzmann Lecture Hall
Associated Event:
Stochastic Partial Differential Equations (Workshop)
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)