Local Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spaces
Local Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spaces
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DOI：
10.1007/s00205-016-1042-7
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发表时间：
2016-02
影响因子：
2.5
通讯作者：
C. Fefferman;D. McCormick;James C. Robinson;José L. Rodrigo
中科院分区：
文献类型：
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作者：
C. Fefferman;D. McCormick;James C. Robinson;José L. Rodrigo
本文建立了具有初值的粘性、非阻磁流体方程解的局部存在唯一性。证明依赖于Stokes方程的最大正则性估计。用初值满足的热方程解不能满足来解释取热障碍；我们给出了这一现象的一个明显的例子。
This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in, whered= 2, 3, with initial dataandforand any. The proof relies on maximal regularity estimates for the Stokes equation. The obstruction to takingis explained by the failure of solutions of the heat equation with initial datato satisfy; we provide an explicit example of this phenomenon.