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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 459, Pages 127–148 (Mi znsl6468)  
On the local smoothness of some class of axi-symmetric solutions to the MHD equations

T. Shilkin

St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia
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Abstract: In this paper we consider a special class of weak axi-symmetric solutions to the MHD equations for which the velocity field has only poloidal component and the magnetic field is toroidal. We prove local regularity for such solutions. The global strong solvability of the initial-boundary value problem for the corresponding system in a cylindrical domain with non-slip boundary conditions for the velocity on the cylindrical surface is established as well.
Key words and phrases: magnetohydrodynamics, axially symmetric solutions, regularity.
Funding agency Grant number
Marie Sklodowska-Curie Actions FP7/2007-2013/
Research Executive Agency (REA) n-319012
Polish Ministry of Science and Higher Education n-2853/7.PR/2013/2
Russian Foundation for Basic Research 17-01-00099-a
The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007-2013/ under REA grant agreement n-319012 and from the Funds for International Co-operation under Polish Ministry of Science and Higher Education grant agreement n-2853/7.PR/2013/2. The author is also supported by RFBR, grant 17-01-00099-a.
Received: 13.08.2017
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 236, Issue 4, Pages 461–475
DOI: https://doi.org/10.1007/s10958-018-4125-1
Document Type: Article
UDC: 517
Language: English
Citation: T. Shilkin, “On the local smoothness of some class of axi-symmetric solutions to the MHD equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 46, Zap. Nauchn. Sem. POMI, 459, POMI, St. Petersburg, 2017, 127–148; J. Math. Sci. (N. Y.), 236:4 (2019), 461–475
Citation in format AMSBIB
\Bibitem{Shi17}
\by T.~Shilkin
\paper On the local smoothness of some class of axi-symmetric solutions to the MHD equations
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~46
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 459
\pages 127--148
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6468}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 236
\issue 4
\pages 461--475
\crossref{https://doi.org/10.1007/s10958-018-4125-1}
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