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

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 518-528.

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

李凯*(),杨晗,王凡

西南交通大学数学学院成都 611756

收稿日期:2018-04-12 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 李凯 E-mail:1033166048@qq.com
基金资助:
国家自然科学基金(11701477)

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

Kai Li*(),Han Yang,Fan Wang

School of Mathematics, Southwest Jiaotong University, Chengdu 611756

Received:2018-04-12 Online:2019-06-26 Published:2019-06-27
Contact: Kai Li E-mail:1033166048@qq.com
Supported by:
the NSFC(11701477)

摘要/Abstract

摘要：

论文研究了带有衰减项的磁流体力学方程组的柯西问题.当 $\beta \ge 1$ 及初值 ${u_0}$ , ${b_0} \in {L^2}({{\mathbb{R} ^3}})$ 时,采用Galerkin方法证明了方程组存在全局弱解.并且当初值 ${u_0} \in H_0^1 \cap {L^{\beta + 1}}({{\mathbb{R} ^3}})$ , ${b_0} \in H_0^1({{\mathbb{R} ^3}})$ 时,可以得到方程组存在唯一局部强解.

关键词: 磁流体力学方程组, 衰减项, 弱解, 强解

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

中图分类号:

O175.29

李凯,杨晗,王凡. 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[J]. 数学物理学报, 2019, 39(3): 518-528.

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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