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# 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

#### 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

Published 19 August 2015