Well-posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics

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Well-posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics. / Trakhinin, Yuri; Wang, Tao.

In: Archive for Rational Mechanics and Analysis, Vol. 239, No. 2, 02.2021, p. 1131-1176.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{aa6c7e60a265462c9cdca2e59e8ff875,

title = "Well-posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics",

abstract = "We consider the free boundary problem for non-relativistic and relativistic ideal compressible magnetohydrodynamics in two and three spatial dimensions with the total pressure vanishing on the plasma–vacuum interface. We establish the local-in-time existence and uniqueness of solutions to this nonlinear characteristic hyperbolic problem under the Rayleigh–Taylor sign condition on the total pressure. The proof is based on certain tame estimates in anisotropic Sobolev spaces for the linearized problem and a modification of the Nash–Moser iteration scheme. Our result is uniform in the speed of light and appears to be the first well-posedness result for the free boundary problem in ideal compressible magnetohydrodynamics with zero total pressure on the moving boundary.",

keywords = "VACUUM INTERFACE PROBLEM, CURRENT-VORTEX SHEETS, EULER EQUATIONS, LOCAL EXISTENCE, MOTION, STABILITY, LIQUID",

author = "Yuri Trakhinin and Tao Wang",

note = "Publisher Copyright: {\textcopyright} 2020, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2021",

month = feb,

doi = "10.1007/s00205-020-01592-6",

language = "English",

volume = "239",

pages = "1131--1176",

journal = "Archive for Rational Mechanics and Analysis",

issn = "0003-9527",

publisher = "Springer New York",

number = "2",

}

RIS

TY - JOUR

T1 - Well-posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics

AU - Trakhinin, Yuri

AU - Wang, Tao

PY - 2021/2

Y1 - 2021/2

N2 - We consider the free boundary problem for non-relativistic and relativistic ideal compressible magnetohydrodynamics in two and three spatial dimensions with the total pressure vanishing on the plasma–vacuum interface. We establish the local-in-time existence and uniqueness of solutions to this nonlinear characteristic hyperbolic problem under the Rayleigh–Taylor sign condition on the total pressure. The proof is based on certain tame estimates in anisotropic Sobolev spaces for the linearized problem and a modification of the Nash–Moser iteration scheme. Our result is uniform in the speed of light and appears to be the first well-posedness result for the free boundary problem in ideal compressible magnetohydrodynamics with zero total pressure on the moving boundary.

AB - We consider the free boundary problem for non-relativistic and relativistic ideal compressible magnetohydrodynamics in two and three spatial dimensions with the total pressure vanishing on the plasma–vacuum interface. We establish the local-in-time existence and uniqueness of solutions to this nonlinear characteristic hyperbolic problem under the Rayleigh–Taylor sign condition on the total pressure. The proof is based on certain tame estimates in anisotropic Sobolev spaces for the linearized problem and a modification of the Nash–Moser iteration scheme. Our result is uniform in the speed of light and appears to be the first well-posedness result for the free boundary problem in ideal compressible magnetohydrodynamics with zero total pressure on the moving boundary.

KW - VACUUM INTERFACE PROBLEM

KW - CURRENT-VORTEX SHEETS

KW - EULER EQUATIONS

KW - LOCAL EXISTENCE

KW - MOTION

KW - STABILITY

KW - LIQUID

UR - http://www.scopus.com/inward/record.url?scp=85096001767&partnerID=8YFLogxK

U2 - 10.1007/s00205-020-01592-6

DO - 10.1007/s00205-020-01592-6

M3 - Article

AN - SCOPUS:85096001767

VL - 239

SP - 1131

EP - 1176

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 2

ER -

ID: 26027969