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

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