We study the free boundary problem for a plasma–vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div‐curl system of pre‐Maxwell dynamics, to better understand the influence of the electric field in vacuum, we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric and magnetic fields. Under the necessary and sufficient stability condition for a planar interface found earlier by Trakhinin, we prove an energy a priori estimate for the linearized constant coefficient problem. The process of derivation of this estimate is based on various methods, including a secondary symmetrization of the vacuum Maxwell equations, the derivation of a hyperbolic evolutionary equation for the interface function, and the construction of a degenerate Kreiss‐type symmetrizer for an elliptic‐hyperbolic problem for the total pressure.

中文翻译：

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真空中具有置换电流的不可压缩等离子体-真空界面的稳定性

我们研究理想不可压缩磁流体动力学中的等离子体-真空界面的自由边界问题。与经典的陈述不同，当真空磁场服从麦克斯韦动力学之前的格线系统时，为了更好地了解真空中电场的影响，我们不忽略真空区域中的位移电流，而是考虑麦克斯韦方程电场和磁场。在Trakhinin较早发现的平面界面的必要和充分稳定性条件下，我们证明了线性常数系数问题的能量先验估计。此估算的推导过程基于多种方法，包括真空麦克斯韦方程的二次对称化，界面函数的双曲演化方程的推导，