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Journal of Mathematical Sciences

, Volume 236, Issue 4, pp 461–475 | Cite as

On the Local Smoothness of Some Class of Axially-Symmetric Solutions to the MHD Equations

  • T. Shilkin
Article
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A special class of weak axially-symmetric solutions to the MHD equations for which the velocity field has only poloidal component and the magnetic field is toroidal is considered. For such solutions a local regularity is proved. The global strong solvability of the initial boundary-value problem for the corresponding system in a cylindrical domain with non-slip boundary conditions for the velocity on the cylindrical surface is established as well.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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