Ergodic results for the stochastic nonlinear Schrödinger equation with large damping
Zdzisław Brzeźniak, Benedetta Ferrario, Margherita Zanella · Journal of Evolution Equations · 2023
Abstract We study a nonlinear Schrödinger equation with a linear damping, i.e. a zero-order dissipation, and an additive noise. Working in $${\mathbb {R}}^d$$ R d with $$d\le 3$$ d ≤ 3 , we prove the uniqueness of the invariant measure when the damping coefficient is sufficiently large.