L3,∞-solutions to the MHD equations

Alex Mahalov, B. Nicolaenko, T. Shilkin

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We prove that weak solutions to the MHD system are smooth provided that they belong to the so-called "critical" Ladyzhenskaya-Prodi-Serrin class L3,∞. Besides the independent interest, this result disproves the hypothesis on existence of collapsing self-similar solutions to the MHD equations for which the generating profile belongs to the space L 3. Thus, we extend the results which were known before for the Navier-Stokes system to the case of the MHD equations. Bibliography: 14 titles.

Original languageEnglish (US)
Pages (from-to)2911-2923
Number of pages13
JournalJournal of Mathematical Sciences
Volume143
Issue number2
DOIs
StatePublished - May 2007

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MHD Equations
Magnetohydrodynamics
Navier-Stokes System
Disprove
Collapsing
Self-similar Solutions
L-space
Weak Solution
Bibliographies
Profile
Bibliography
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

L3,∞-solutions to the MHD equations. / Mahalov, Alex; Nicolaenko, B.; Shilkin, T.

In: Journal of Mathematical Sciences, Vol. 143, No. 2, 05.2007, p. 2911-2923.

Research output: Contribution to journalArticle

Mahalov, Alex ; Nicolaenko, B. ; Shilkin, T. / L3,∞-solutions to the MHD equations. In: Journal of Mathematical Sciences. 2007 ; Vol. 143, No. 2. pp. 2911-2923.
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