L3,∞-solutions to the MHD equations

Alex Mahalov, B. Nicolaenko, T. Shilkin

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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
Issue number2
StatePublished - May 2007

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Applied Mathematics


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