Реферат: We consider the two-dimensional plasma-vacuum interface problem in ideal compressible magnetohydrodynamics (MHD). This is a hyperbolic-elliptic coupled system with a characteristic free boundary. In the plasma region the 2D planar flow is governed by the hyperbolic equations of ideal compressible MHD, while in the vacuum region the magnetic field obeys the elliptic system of pre-Maxwell dynamics. At the free interface moving with the velocity of plasma particles, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. The plasma-vacuum system is not isolated from the outside world, since it is driven by a given surface current which forces oscillations onto the system. We prove the local-in-time existence and uniqueness of solutions to this nonlinear free boundary problem, provided that at least one of the two magnetic fields, in the plasma or in the vacuum region, is non-zero at each point of the initial interface. The proof follows from the analysis of the linearized MHD equations in the plasma region and the elliptic system for the vacuum magnetic field, suitable tame estimates in Sobolev spaces for the full linearized problem, and a Nash–Moser iteration.

Библиографическая ссылка: Morando A. , Secchi P. , Trakhinin Y. , Trebeschi P. , Yuan D.
Well-Posedness of the Two-Dimensional Compressible Plasma-Vacuum Interface Problem
Archive for Rational Mechanics and Analysis. 2024. V.248. N4. 56 :1-45. DOI: 10.1007/s00205-024-02001-y WOS Scopus РИНЦ OpenAlex

Даты:

Поступила в редакцию:	18 июл. 2023 г.
Принята к публикации:	8 мая 2024 г.
Опубликована в печати:	4 июн. 2024 г.
Опубликована online:	4 июн. 2024 г.

Идентификаторы БД:

Web of science:	WOS:001238676800001
Scopus:	2-s2.0-85195403852
РИНЦ:	68061756
OpenAlex:	W4399329352

Цитирование в БД:

БД	Цитирований
Scopus	1
OpenAlex	1

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