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 L3. Thus, we extend the results which were known before for the Navier-Stokes system to the case of the MHD equations. Bibliography: 14 titles.
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