Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 518-528.

Previous Articles     Next Articles

Study on Weak Solution and Strong Solution of Incompressible MHD Equations with Damping in Three-Dimensional Systems

Kai Li*(),Han Yang,Fan Wang   

  1. School of Mathematics, Southwest Jiaotong University, Chengdu 611756
  • Received:2018-04-12 Online:2019-06-26 Published:2019-06-27
  • Contact: Kai Li
  • Supported by:
    the NSFC(11701477)


In this paper, the Cauchy problem of the MHD equations with damping is studied. When $\beta \ge 1$ and initial data satisfy ${u_0}$, ${b_0} \in {L^2}({{\mathbb{R} ^3}})$, the Galerkin method is used to prove the global weak solution of the equations. When the initial data satisfy ${u_0} \in H_0^1 \cap {L^{\beta + 1}}({{\mathbb{R} ^3}})$, ${b_0} \in H_0^1({{\mathbb{R} ^3}})$, it is possible to obtain a unique local strong solution for the equation group.

Key words: MHD equations, Damping, Weak solutions, Strong solutions

CLC Number: 

  • O175.29