Well-Posedness for Stochastic Nonlinear Schrödinger Equations with Rotation

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发表日期：

2025年9月1日

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Jian Wang,
Jianliang Zhai,
Tusheng Zhang

摘要

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 $\textrm{It}\hat{o}$ $It \hat{o}$ formula for the $L^p$ $L^{p}$ and Sobolev norms of the solution.