Global energy solutions to a stochastic Schrödinger-Poisson system with multiplicative noise in two dimensions

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• 作者：Lixin Meng^a ; ^b ; ^{menglx790@nenu.edu.cn} ; Jingyu Li^b ; ^{lijy645@nenu.edu.cn} ; Jian Tao^b ; ^{taoj@nenu.edu.cn}
• 关键词：Schrö ; dinger&ndash ; Poisson system ; Stochastic partial differential equations ; White noise ; Global solutions ; Commutator estimates
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：300
• 期：Complete
• 页码：40-59
• 全文大小：669 K
• 卷排序：300

文摘

We are concerned with the Cauchy problem for a two-dimensional stochastic Schrödinger–Poisson system with a multiplicative noise in the energy space. Depending on the values of the physical parameters, this system models a self-gravitating Bose–Einstein condensate of the dark matter in the universe or the electron transport in semiconductors under the effect of thermal fluctuations. We show that in both cases the system admits a unique global solution in H1. The key ingredient of this paper is to establish appropriate commutator estimates for the multiplicative noise.