Well-Posedness for Stochastic Nonlinear Schrödinger Equations with Rotation

Abstract

We establish the existence and uniqueness of solutions of stochastic nonlinear Schrödinger equations with rotation in a weighted Sobolev space. In order to obtain the global well-posedness, we need some a priori estimates for the energy of the solution, which requires a careful analysis of the commutators involved. An important role is also played by the $\textrm{It}\hat{o}$ formula for the $L^p$ and Sobolev norms of the solution.

Keywords

Stochastic nonlinear Schrödinger equations / Mild/variational solutions / Strichartz estimates / Weighted Sobolev space / Energy estimates / 60H15 / 35B65 / 35J10

Funding

National Natural Science Foundation of China-China Academy of General Technology Joint Fund for Basic Research(11971456, 11721101)

School Start-up Fund (USTC)(KY0010000036)

the Fundamental Research Funds for the Central Universities(WK3470000016)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature