Local and global well-posedness of 2d periodic multiplicative stochastic NLS

TL;DR

This paper proves the global well-posedness of a 2D periodic multiplicative stochastic nonlinear Schrödinger equation with rough potentials like spatial white noise, using Strichartz estimates to control solution norms.

Contribution

It establishes the first global well-posedness results for this class of stochastic NLS with rough potentials on the 2D torus, including energy and strong regimes.

Findings

Global well-posedness proven for stochastic NLS with white noise potential

Controls established over the growth of solution norms

Applicable to general integer powers in the equation

Abstract

We use Strichartz estimates with rough potentials like the spatial white noise on the 2 \ dimensional torus to prove global well-posedness of the multiplicative stochastic NLS with general integer powers in both the energy and strong regime together with controls over the growth of the norms of the solutions.