Seminar| Institute of Mathematical Sciences
Time: Monday, October 19th, 2026,13:00-14:00
Location: IMS S408
Speaker: Tianyi Pan, NYU Shanghai
Abstract: We consider the weakly damped stochastic nonlinear Schrodinger equation on the real line, driven by a noise that is white in time and smooth in space. Assuming that the noise is sufficiently non-degenerate, we prove that the equation has a unique stationary measure in the class of probability measures concentrated on H, and establish polynomial mixing in the dual-Lipschitz metric over H1. We do not impose any restriction on the size of the damping.
The proof is based on a coupling argument, whose key ingredient is a Foias-Prodi-type estimate in the H1-norm, derived by means of a Lyapunov functional adapted to the linearized NLS dynamics. To compensate for the loss of compactness, we combine this estimate with a truncated Poincare inequality and a space-time weight function quantifying the spatial decay of solutions.