三维带有衰减项的不可压缩磁流体力学方程组弱解与强解的研究

Abstract

Abstract:

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

Kai Li,Han Yang,Fan Wang. Study on Weak Solution and Strong Solution of Incompressible MHD Equations with Damping in Three-Dimensional Systems[J].Acta mathematica scientia,Series A, 2019, 39(3): 518-528.

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References 11

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

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