About well-posedness of a free boundary problem for ideal compressible MHD equations and Maxwell equations in vacuum | Sciact - Система учета научной деятельности ИМ СО РАН

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

Журнал

Journal of Mathematical Sciences (United States)
ISSN: 1072-3374 , E-ISSN: 1573-8795

Вых. Данные

Год: 2025, Том: 293, Номер: 4, Страницы: 601-616 Страниц : 16 DOI: 10.1007/s10958-025-08028-0

Ключевые слова

ideal compressible magnetohydrodynamics equations, free boundary problem, displacement current, Maxwell’s equations, nonlinear hyperbolic problem, well-posedness

Авторы

Trakhinin Yu.L. ¹

Организации

1	Sobolev Institute of Mathematics, Novosibirsk, Russia

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0008

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.

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

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

Опубликована в печати:	25 окт. 2025 г.
Опубликована online:	25 окт. 2025 г.

Scopus:	2-s2.0-105019659712
OpenAlex:	W4415533880

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