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About well-posedness of a free boundary problem for ideal compressible MHD equations and Maxwell equations in vacuum Full article

Journal Journal of Mathematical Sciences (United States)
ISSN: 1072-3374 , E-ISSN: 1573-8795
Output data Year: 2025, Volume: 293, Number: 4, Pages: 601-616 Pages count : 16 DOI: 10.1007/s10958-025-08028-0
Tags ideal compressible magnetohydrodynamics equations, free boundary problem, displacement current, Maxwell’s equations, nonlinear hyperbolic problem, well-posedness
Authors Trakhinin Yu.L. 1
Affiliations
1 Sobolev Institute of Mathematics, Novosibirsk, Russia

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0008

Abstract: 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.
Cite: Trakhinin Y.L.
About well-posedness of a free boundary problem for ideal compressible MHD equations and Maxwell equations in vacuum
Journal of Mathematical Sciences (United States). 2025. V.293. N4. P.601-616. DOI: 10.1007/s10958-025-08028-0 Scopus OpenAlex
Original: Трахинин Ю.Л.
О корректности задачи со свободной границей для уравнений идеальной сжимаемой МГД и уравнений максвелла в вакууме
Современная математика. Фундаментальные направления. 2025. Т.71. №1. С.176-193. DOI: 10.22363/2413-3639-2025-71-1-176-193 РИНЦ OpenAlex
Dates:
Published print: Oct 25, 2025
Published online: Oct 25, 2025
Identifiers:
Scopus: 2-s2.0-105019659712
OpenAlex: W4415533880
Citing: Пока нет цитирований
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