Global well posedness and ergodic results in regular Sobolev spaces for the nonlinear Schrödinger equation with multiplicative noise and arbitrary power of the nonlinearity

Zdzisław Brzeźniak, Benedetta Ferrario, Mario Maurelli +1

We consider the nonlinear Schrödinger equation on the $d$-dimensional torus ${\mathbb{T}}^d$, with the nonlinearity of polynomial type $|u{|}^{2\sigma }u$. For any $\sigma \in \mathbb{N}$ and $s>\fr…