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 |
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| 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 |
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| Affiliations |
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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
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
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:
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