Global martingale solution to the stochastic nonhomogeneous magnetohydrodynamics system. (English) Zbl 1375.35644

Yamazaki, Kazuo

Adv. Differ. Equ. 21, No. 11-12, 1085-1116 (2016).

Summary: 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.

MSC:

35R60	PDEs with randomness, stochastic partial differential equations
35Q35	PDEs in connection with fluid mechanics
35R45	Partial differential inequalities and systems of partial differential inequalities
76W05	Magnetohydrodynamics and electrohydrodynamics
60H15	Stochastic partial differential equations (aspects of stochastic analysis)