On the stochastic nonlinear Schrödinger equations with non-smooth additive noise

Abstract

We study the stochastic nonlinear Schrödinger equations with additive stochastic forcing. By using the dispersive estimate, we present a simple argument, constructing a unique local-in-time solution with rougher stochastic forcing than those considered in the literature.

14 pages. To appear in Kyoto J. Math

References in corpus (2)

• Random data Cauchy theory for supercritical wave equations I: Local theory
• Almost sure local well-posedness for the supercritical quintic NLS

Cited by in corpus (2)

• Global well-posedness of the energy-critical stochastic nonlinear wave equations
• Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation