Existence of Compressible Current-Vortex Sheets: Variable Coefficients Linear Analysis
Existence of Compressible Current-Vortex Sheets: Variable Coefficients Linear Analysis
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DOI：
10.1007/s00205-005-0364-7
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发表时间：
2005-04
影响因子：
2.5
通讯作者：
Y. Trakhinin
中科院分区：
文献类型：
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作者：
Y. Trakhinin
我们研究了由理想可压缩磁流体动力学方程的线性化和非定常分段光滑解的朗肯-于贡尼奥关系所产生的初始边值问题。该解被认为是切向不连续表面（电流涡流片）两侧磁流体动力学系统的经典解。在对未扰动流的一些假设下，我们证明了线性化问题的能量优先估计。由于切向不连续性是特征，因此函数设置由各向异性加权 Sobolev 空间 W21,σ 提供。尽管常系数线性化问题不满足均匀 Kreiss-Lopatinskii 条件，但即使对于变系数问题和非平面电流涡流片，我们获得的估计也不会损失平滑度。本文的结果是证明磁流体动力学非线性方程的电流涡片解的局部时间存在性的必要步骤。
We study the initial-boundary value problem resulting from the linearization of the equations of ideal compressible magnetohydrodynamics and the Rankine-Hugoniot relations about an unsteady piecewise smooth solution. This solution is supposed to be a classical solution of the system of magnetohydrodynamics on either side of a surface of tangential discontinuity (current-vortex sheet). Under some assumptions on the unperturbed flow, we prove an energya prioriestimate for the linearized problem. Since the tangential discontinuity is characteristic, the functional setting is provided by the anisotropic weighted Sobolev spaceW21,σ. Despite the fact that the constant coefficients linearized problem does not meet the uniform Kreiss-Lopatinskii condition, the estimate we obtain is without loss of smoothness even for the variable coefficients problem and nonplanar current-vortex sheets. The result of this paper is a necessary step in proving the local-in-time existence of current-vortex sheet solutions of the nonlinear equations of magnetohydrodynamics.