Advances in Differential Equations

Global martingale solution to the stochastic nonhomogeneous magnetohydrodynamics system

Kazuo Yamazaki

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We study the three-dimensional stochastic nonhomogeneous magnetohydrodynamics system with random external forces that involve feedback, i.e., multiplicative noise, and are non-Lipschitz. We prove the existence of a global martingale solution via a semi-Galerkin approximation scheme with stochastic calculus and applications of Prokhorov's and Skorokhod's theorems. Furthermore, using de Rham's theorem for processes, we prove the existence of the pressure term.

Article information

Adv. Differential Equations, Volume 21, Number 11/12 (2016), 1085-1116.

First available in Project Euclid: 13 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics 35R45: Partial differential inequalities 60H15: Stochastic partial differential equations [See also 35R60]


Yamazaki, Kazuo. Global martingale solution to the stochastic nonhomogeneous magnetohydrodynamics system. Adv. Differential Equations 21 (2016), no. 11/12, 1085--1116.

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