Well-Posedness for Stochastic Nonlinear Schrödinger Equations with Rotation

Jian Wang , Jianliang Zhai , Tusheng Zhang

Communications in Mathematics and Statistics ›› : 1 -30.

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Communications in Mathematics and Statistics ›› : 1 -30. DOI: 10.1007/s40304-025-00451-8
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Well-Posedness for Stochastic Nonlinear Schrödinger Equations with Rotation

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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

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Jian Wang,Jianliang Zhai,Tusheng Zhang. Well-Posedness for Stochastic Nonlinear Schrödinger Equations with Rotation. Communications in Mathematics and Statistics 1-30 DOI:10.1007/s40304-025-00451-8

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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)

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

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