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



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


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.


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