Stochastic logarithmic Schrödinger equations : energy regularized approach

Abstract

In this paper, we prove the global existence and uniqueness of the solution of the stochastic logarithmic Schrödinger (SlogS) equation driven by either additive noise or multiplicative noise. The key ingredient lies in the regularized SlogS (RSlogS) equation with regularized energy and the strong convergence analysis of the solutions of the RSlogS equations. In addition, temporal Hölder regularity estimates and uniform estimates in energy space [text could not be shown] and weighted Sobolev space [text could not be shown] of the solutions for both the SlogS equation and RSlogS equation are also obtained. [Abstract not complete, refer to publisher pdf]