THE FREE INTERFACE PROBLEM OF PLASMA-VACUUM WITH SURFACE TENSION IN A TUBE DOMAIN

doi:10.1007/s10473-025-0405-2

摘要/Abstract

摘要： In this paper, we consider the plasma-vacuum interface problem in a cylindrical tube region impressed by a special background magnetic field. The interior region is occupied with plasma, which is governed by the incompressible inviscid and resistive MHD system without damping term. The exterior vacuum region is governed by the so-called the ``pre-Maxwell equations". And on the free interface, additionally, the effect of surface tension is taken into account. The original region can be transformed into a horizontally periodic slab through the cylindrical coordinate transformation, which will be impressed by a uniform non-horizontal magnetic field. Appending with the appropriate physical boundary conditions, the global well-posedness of the problem is established by the energy method.

关键词: MHD, the free interface problem, energy estimates, global solution, local well-posedness

Abstract: In this paper, we consider the plasma-vacuum interface problem in a cylindrical tube region impressed by a special background magnetic field. The interior region is occupied with plasma, which is governed by the incompressible inviscid and resistive MHD system without damping term. The exterior vacuum region is governed by the so-called the ``pre-Maxwell equations". And on the free interface, additionally, the effect of surface tension is taken into account. The original region can be transformed into a horizontally periodic slab through the cylindrical coordinate transformation, which will be impressed by a uniform non-horizontal magnetic field. Appending with the appropriate physical boundary conditions, the global well-posedness of the problem is established by the energy method.

Key words: MHD, the free interface problem, energy estimates, global solution, local well-posedness

Biran ZHANG. THE FREE INTERFACE PROBLEM OF PLASMA-VACUUM WITH SURFACE TENSION IN A TUBE DOMAIN[J]. 数学物理学报(英文版), 2025, 45(4): 1307-1342.

Biran ZHANG. THE FREE INTERFACE PROBLEM OF PLASMA-VACUUM WITH SURFACE TENSION IN A TUBE DOMAIN[J]. Acta mathematica scientia,Series B, 2025, 45(4): 1307-1342.

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