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.
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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
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