Martingale solutions of the stochastic Hall-magnetohydrodynamics equations on ℝ³

2021/09/13 by Elżbieta Motyl, Motyl, Elżbieta
Economics, Econometrics and Finance · Mathematics · #35Q30 #76M35 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications #primary 35Q35 #secondary 60H15

paper · pdf · doi:10.48550/arxiv.2109.06297

openalex publication_date 2021/09/13 · openalex created_date 2021/09/27 · openalex updated_date 2026/07/28

Abstract

We prove the existence of a global martingale solution of a stochastic Hall-magnetohydrodynamics equations on ℝ³ with multiplicative noise. Using the Fourier analysis we construct a sequence of approximate solutions. The existence of a solution is proved via the stochastic compactness method and the Jakubowski generalization of the Skorokhod theorem for nonmetric spaces, in particular, the spaces with weak topologies. The main difficulty is caused by the Hall term which makes the equations strongly nonlinear.

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