Stochastic Hall-Magneto-hydrodynamics System in Three and Two and a Half Dimensions

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• 作者：Kazuo Yamazaki
• 关键词：Hall ; magneto ; hydrodynamics system ; Martingale representation theorem ; Prokhorov’s theorem ; Skorokhod’s theorem
• 刊名：Journal of Statistical Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：166
• 期：2
• 页码：368-397
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics;
• 出版者：Springer US
• ISSN：1572-9613
• 卷排序：166

文摘

We introduce the stochastic Hall-magneto-hydrodynamics (Hall-MHD) system in three and two and a half dimensions with infinite-dimensional multiplicative noise, white in time, and prove the global existence of a martingale solution via a stochastic Galerkin approximation and applications of Prokhorov’s, Skorokhod’s and martingale representation theorems, as well as the pressure term through de Rham’s theorem adapted to processes. The Hall term represents mathematically a very singular nonlinear term, unprecedented in the previous work. The results extend many others on the deterministic Hall-MHD and stochastic MHD systems and Navier–Stokes equations. In contrast to the stochastic MHD system, the path-wise uniqueness in the two and a half dimensional case is an open problem.