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Journal of Statistical Physics

, Volume 166, Issue 2, pp 368–397 | Cite as

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

  • Kazuo Yamazaki
Article

Abstract

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.

Keywords

Hall-magneto-hydrodynamics system Martingale representation theorem Prokhorov’s theorem Skorokhod’s theorem 

Mathematics Subject Classification

35Q35 37L55 60H15 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA

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