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Global martingale solution to the stochastic nonhomogeneous magnetohydrodynamics system

Kazuo Yamazaki
- 01 Nov 2016 - 
- Vol. 21, pp 1085-1116
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TLDR
In this paper, 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 was proved.
Abstract
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.

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Stochastic MHD equations with fractional kinematic dissipation and partial magnetic diffusion in R2

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Large deviation principle for the micropolar, magneto-micropolar fluid systems

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Ergodicity of a Galerkin approximation of three-dimensional magnetohydrodynamics system forced by a degenerate noise

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