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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Volume 62, Issue 4, Pages 181–190
DOI: https://doi.org/10.15372/PMTF20210418 (Mi pmtf141) 		 
Local solvability of problems with free boundaries in the magnetic hydrodynamics of an ideal compressible fluid with and without account for surface tension

Yu. L. Trakhinin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.15372/PMTF20210418
Abstract: Data are presented on time-local solvability of problems with free boundaries for a system of equations of magnetohydrodynamics of an ideal compressible fluid. A problem with a free plasma-vacuum boundary and a problem with boundary conditions on a contact discontinuity are considered. A scheme is given for proving the local existence and uniqueness of smooth solutions of these problems with and without account for surface tension.
Keywords: magnetohydrodynamics, free boundary problem, surface tension, local theorem of existence and uniqueness.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00261
Received: 11.05.2021
Revised: 17.05.2021
Accepted: 31.05.2021
English version:
Journal of Applied Mechanics and Technical Physics, 2021, Volume 62, Issue 4, Pages 684–691
DOI: https://doi.org/10.1134/S0021894421040180
Bibliographic databases:
Document Type: Article
UDC: 517.956.35, 537.84
Language: Russian
Citation: Yu. L. Trakhinin, “Local solvability of problems with free boundaries in the magnetic hydrodynamics of an ideal compressible fluid with and without account for surface tension”, Prikl. Mekh. Tekh. Fiz., 62:4 (2021), 181–190; J. Appl. Mech. Tech. Phys., 62:4 (2021), 684–691
Citation in format AMSBIB
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\by Yu.~L.~Trakhinin
\paper Local solvability of problems with free boundaries in the magnetic hydrodynamics of an ideal compressible fluid with and without account for surface tension
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2021
\vol 62
\issue 4
\pages 181--190
\mathnet{http://mi.mathnet.ru/pmtf141}
\crossref{https://doi.org/10.15372/PMTF20210418}
\elib{https://elibrary.ru/item.asp?id=46448004}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2021
\vol 62
\issue 4
\pages 684--691
\crossref{https://doi.org/10.1134/S0021894421040180}
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