The stochastic logarithmic Schrödinger equation

Abstract

In this paper we prove global existence and uniqueness of solutions to the stochastic logarithmic Schrödinger equation with linear multiplicative noise. Our approach is mainly based on the rescaling approach and the method of maximal monotone operators. In addition, uniform estimates of solutions in the energy space $H^1(\mathbb{R}^d)$ and in an appropriate Orlicz space are also obtained here.