Well-posedness for the free-boundary ideal compressible magnetohydrodynamic equations with surface tension

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Well-posedness for the free-boundary ideal compressible magnetohydrodynamic equations with surface tension. / Trakhinin, Yuri; Wang, Tao.

In: Mathematische Annalen, Vol. 383, No. 1-2, 06.2022, p. 761-808.

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

BibTeX

@article{b088deed444a48f1b0266c1af989e718,

title = "Well-posedness for the free-boundary ideal compressible magnetohydrodynamic equations with surface tension",

abstract = "We establish the local existence and uniqueness of solutions to the free-boundary ideal compressible magnetohydrodynamic equations with surface tension in three spatial dimensions by a suitable modification of the Nash–Moser iteration scheme. The main ingredients in proving the convergence of the scheme are the tame estimates and unique solvability of the linearized problem in the anisotropic Sobolev spaces H∗m for m large enough. In order to derive the tame estimates, we make full use of the boundary regularity enhanced from the surface tension. The unique solution of the linearized problem is constructed by designing some suitable ε–regularization and passing to the limit ε→ 0.",

keywords = "Free boundary problem, Ideal compressible magnetohydrodynamics, Nash–Moser iteration, Surface tension, Well-posedness",

author = "Yuri Trakhinin and Tao Wang",

note = "Funding Information: The research of Yuri Trakhinin was supported by Mathematical Center in Akademgorodok under Agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation. The research of Tao Wang was partially supported by the National Natural Science Foundation of China under Grants 11971359 and 11731008. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2022",

month = jun,

doi = "10.1007/s00208-021-02180-z",

language = "English",

volume = "383",

pages = "761--808",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "1-2",

}

RIS

TY - JOUR

T1 - Well-posedness for the free-boundary ideal compressible magnetohydrodynamic equations with surface tension

AU - Trakhinin, Yuri

AU - Wang, Tao

N1 - Funding Information: The research of Yuri Trakhinin was supported by Mathematical Center in Akademgorodok under Agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation. The research of Tao Wang was partially supported by the National Natural Science Foundation of China under Grants 11971359 and 11731008. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2022/6

Y1 - 2022/6

N2 - We establish the local existence and uniqueness of solutions to the free-boundary ideal compressible magnetohydrodynamic equations with surface tension in three spatial dimensions by a suitable modification of the Nash–Moser iteration scheme. The main ingredients in proving the convergence of the scheme are the tame estimates and unique solvability of the linearized problem in the anisotropic Sobolev spaces H∗m for m large enough. In order to derive the tame estimates, we make full use of the boundary regularity enhanced from the surface tension. The unique solution of the linearized problem is constructed by designing some suitable ε–regularization and passing to the limit ε→ 0.

AB - We establish the local existence and uniqueness of solutions to the free-boundary ideal compressible magnetohydrodynamic equations with surface tension in three spatial dimensions by a suitable modification of the Nash–Moser iteration scheme. The main ingredients in proving the convergence of the scheme are the tame estimates and unique solvability of the linearized problem in the anisotropic Sobolev spaces H∗m for m large enough. In order to derive the tame estimates, we make full use of the boundary regularity enhanced from the surface tension. The unique solution of the linearized problem is constructed by designing some suitable ε–regularization and passing to the limit ε→ 0.

KW - Free boundary problem

KW - Ideal compressible magnetohydrodynamics

KW - Nash–Moser iteration

KW - Surface tension

KW - Well-posedness

UR - http://www.scopus.com/inward/record.url?scp=85104865836&partnerID=8YFLogxK

U2 - 10.1007/s00208-021-02180-z

DO - 10.1007/s00208-021-02180-z

M3 - Article

AN - SCOPUS:85104865836

VL - 383

SP - 761

EP - 808

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1-2

ER -

ID: 28464660