BKM's Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero Viscosity
BKM's Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero Viscosity
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DOI：
10.3934/dcds.2009.25.575
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发表时间：
2009-01
期刊：
影响因子：
--
通讯作者：
Zhen Lei;Yi Zhou
中科院分区：
文献类型：
--
作者：
Zhen Lei;Yi Zhou
本文导出了$\mathbb{R}^3$中具有零黏度和正电阻率的不可压缩磁流体动力学方程经典解的击穿判据。这个结果类似于著名的Beale-Kato-Majda的不可压缩流体的无粘Eluer方程的击穿判据。在$\mathbb{R}^2$中，我们建立了Sobolev空间$H^1(\mathbb{R}^2)$中初始数据具有零粘度和正电阻率的磁流体动力学方程的全局弱解。
In this paper we derive a criterion for the breakdown of classical solutions to the incompressible magnetohydrodynamic equations with zero viscosity and positive resistivity in $\mathbb{R}^3$. This result is analogous to the celebrated Beale-Kato-Majda's breakdown criterion for the inviscid Eluer equations of incompressible fluids. In $\mathbb{R}^2$ we establish global weak solutions to the magnetohydrodynamic equations with zero viscosity and positive resistivity for initial data in Sobolev space $H^1(\mathbb{R}^2)$.