Advances in Differential Equations

Global martingale solution to the stochastic nonhomogeneous magnetohydrodynamics system

Kazuo Yamazaki

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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.

Article information

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

Dates
First available in Project Euclid: 13 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.ade/1476369297

Mathematical Reviews number (MathSciNet)
MR3556761

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

Citation

Yamazaki, Kazuo. Global martingale solution to the stochastic nonhomogeneous magnetohydrodynamics system. Adv. Differential Equations 21 (2016), no. 11/12, 1085--1116. https://projecteuclid.org/euclid.ade/1476369297.


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