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 language||English (US)|
|Number of pages||13|
|Journal||Journal of Mathematical Sciences|
|State||Published - May 2007|
ASJC Scopus subject areas
- Statistics and Probability
- Applied Mathematics