Communications in Mathematical Sciences

Volume 13 (2015)

Number 7

On the global well-posedness of the magnetic-curvature-driven plasma equations with random effects in $\mathbb{R}^3$

Pages: 1665 – 1681

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n7.a2

Author

Xinglong Wu (Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, China)

Abstract

The present paper is devoted to the study of the Cauchy problem for the magneticcurvature-driven electromagnetic fluid equation with random effects in a bounded domain of $\mathbb{R}^3$. We first obtain a crucial property of the solution to the O.U. process. Thanks to the lemma, the local well-posedness of the equation with the initial and boundary value is established by the contraction mapping argument. Finally, by virtue of a priori estimates, the existence and uniqueness of a global solution to the stochastic plasma equation is proven.

Keywords

magnetic-curvature-driven plasma equations with random effects, electromagnetic fluid, Cauchy problem, well-posedness, global existence of solution

2010 Mathematics Subject Classification

35R60, 76W05

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Published 19 August 2015