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<p>In this paper, we consider results on the well-posedness of the free interface problem with an interface separating a perfectly conducting inviscid fluid (e.g., plasma) from the vacuum. The flow of fluid is described by the equations of ideal compressible magnetohydrodynamics (MHD). Unlike the classical problem setting, where the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do not neglect the displacement current in the vacuum domain and consider the Maxwell equations for electric and magnetic fields. Combined with boundary conditions on the interface, this forms a nonlinear hyperbolic problem with a characteristic free boundary. Such a free boundary problem comes from the relativistic setting, where the displacement current in vacuum cannot be neglected. We also briefly survey the recent results showing the stabilizing effect of surface tension.</p>

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ABOUT WELL-POSEDNESS OF A FREE BOUNDARY PROBLEM FOR IDEAL COMPRESSIBLE MHD EQUATIONS AND MAXWELL EQUATIONS IN VACUUM

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Yu. L. Trakhinin

摘要

In this paper, we consider results on the well-posedness of the free interface problem with an interface separating a perfectly conducting inviscid fluid (e.g., plasma) from the vacuum. The flow of fluid is described by the equations of ideal compressible magnetohydrodynamics (MHD). Unlike the classical problem setting, where the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do not neglect the displacement current in the vacuum domain and consider the Maxwell equations for electric and magnetic fields. Combined with boundary conditions on the interface, this forms a nonlinear hyperbolic problem with a characteristic free boundary. Such a free boundary problem comes from the relativistic setting, where the displacement current in vacuum cannot be neglected. We also briefly survey the recent results showing the stabilizing effect of surface tension.