STOCHASTIC LOGARITHMIC SCHRODINGER EQUATIONS: ENERGY REGULARIZED APPROACH

In this paper, we prove the global existence and uniqueness of the solution of the stochastic logarithmic Schrodinger (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 Holder regularity estimates and uniform estimates in energy space H-1(O) and weighted Sobolev space L-alpha(2) (O) of the solutions for both the SlogS equation and RSlogS equation are also obtained.

Automated summary

This paper proves the global existence and uniqueness of the solution of the stochastic logarithmic Schrodinger equation driven by either additive noise or multiplicative noise. The key lies in the regularized logarithmic Schrodinger equation with regularized energy and the strong convergence analysis of the solutions. In addition, temporal Holder regularity estimates and uniform estimates in energy space and weighted Sobolev space are obtained for the solutions of both the original and the regularized equation.