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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 336, Pages 112–132 (Mi znsl199)  
This article is cited in 27 scientific papers (total in 27 papers)

$L_{3,\infty}$-solutions to the MHD equations

A. Mahalova, B. Nicolaenko, T. N. Shilkinb

a Arizona State University
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (260 kB) Citations (27)
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Abstract: We prove that weak solutions to the MHD system are smooth providing they belong to the so-called “critical” Ladyzhenskaya–Prodi–Serrin class $L_{3,\infty}$. Besides the independent interest, this result controverts the hypothesis on the existence of collapsing self-similar solutions to the MHD equations for which the generating profile belongs to the space $L_3$. So, we extend the results that were known before for the Navier–Stokes system, for the case of the MHD equations.
Received: 06.03.2006
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 143, Issue 2, Pages 2911–2923
DOI: https://doi.org/10.1007/s10958-007-0175-5
Bibliographic databases:
UDC: 517
Language: English
Citation: A. Mahalov, B. Nicolaenko, T. N. Shilkin, “$L_{3,\infty}$-solutions to the MHD equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Zap. Nauchn. Sem. POMI, 336, POMI, St. Petersburg, 2006, 112–132; J. Math. Sci. (N. Y.), 143:2 (2007), 2911–2923
Citation in format AMSBIB
\Bibitem{MahNicShi06}
\by A.~Mahalov, B.~Nicolaenko, T.~N.~Shilkin
\paper $L_{3,\infty}$-solutions to the MHD equations
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~37
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 336
\pages 112--132
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl199}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2270882}
\zmath{https://zbmath.org/?q=an:1127.35047}
\elib{https://elibrary.ru/item.asp?id=9307456}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 143
\issue 2
\pages 2911--2923
\crossref{https://doi.org/10.1007/s10958-007-0175-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247363522}
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    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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