Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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
References:
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}
Linking options:
  • https://www.mathnet.ru/eng/znsl199
  • https://www.mathnet.ru/eng/znsl/v336/p112
  • 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
    Записки научных семинаров ПОМИ
    Statistics & downloads:
    Abstract page:291
    Full-text PDF :124
    References:51
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024