二维理想不可压缩MHD等离子体-真空自由边界问题的全局非线性稳定性
Global nonlinear stability of the plasma-vacuum free boundary problem for the 2D ideal incompressible MHD
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中文总结 AI 辅助
针对二维理想不可压缩MHD等离子体-真空自由边界问题，在强水平磁场下证明了全局时间非线性稳定性，核心方法依赖对内部流体与界面动力学相互作用及问题内在结构的分析。
中文摘要 AI 辅助
我们研究二维空间中的等离子体-真空界面问题。等离子体区域由理想不可压缩磁流体动力学方程控制。真空区域由前麦克斯韦动力学描述，为简化起见，未知量设为零。这是一个理想欧拉型方程的自由边界问题。在等离子体区域存在强水平磁场的条件下，我们证明了二维等离子体-真空界面的全局时间非线性稳定性。证明依赖于理解域内流体动力学与自由界面上动力学之间的相互作用，以及问题本身的内在结构。
英文摘要
We address the plasma-vacuum interface problem in the two dimensional space. The plasma region is governed by the ideal incompressible magnetohydrodynamic equations. The vacuum region is described by the pre-Maxwell dynamics, with the unknowns set to zero for simplicity. This is a free boundary problem of ideal Euler type equations. Under the strong horizontal magnetic field in the plasma region, we prove the global in time nonlinear stability of the two dimensional plasma-vacuum interface. The proof relies on understanding the interplay between the dynamics of the fluids inside the domain and those on the free interface, as well as the inherent structures of the problem.
发表机构
- Fudan University（复旦大学）
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