Abstract
We consider a free boundary problem for the two-dimensional plasma-vacuum interface ideal magnetohydrodynamic (MHD) flows. In the plasma region, the flow is governed by the compressible ideal MHD equations, while in the vacuum region, we consider the full-Maxwell equations for the electric and the magnetic fields. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. We establish a linear stability/instability criterion of equilibrium state for the Rayleigh-Taylor (RT) problem and the linear stability for the ideal MHD equations. More specifically, we study the stabilizing effect of impressed magnetic fields upon solutions to the equations obtained by linearization around the equilibrium state. We give the critical magnetic number \(H_c\) by a modified variational method and prove that the linearized system is stable when the horizontal impressed magnetic field \({\bar{H}}=({\bar{H}}_1,0)\) satisfies \(|{\bar{H}}_1|>H_c\), while unstable for \(|{\bar{H}}_1|<H_c\).
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Acknowledgements
The research of Yichen Dai is supported by National Key R &D Program of China (No. 2021YFA1002900).
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The research of Yichen Dai is supported by National Key R &D Program of China (No. 2021YFA1002900).
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Dai, Y. The Linear Stability of the Two-dimensional Plasma-vacuum Interface Problem. J Dyn Diff Equat (2023). https://doi.org/10.1007/s10884-023-10256-4
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DOI: https://doi.org/10.1007/s10884-023-10256-4