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

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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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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    T. Shilkin

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  1. T. Shilkin
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Correspondence to T. Shilkin.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 459, 2017, pp. 127–148.

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Shilkin, T. On the Local Smoothness of Some Class of Axially-Symmetric Solutions to the MHD Equations. J Math Sci 236, 461–475 (2019). https://doi.org/10.1007/s10958-018-4125-1

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  • DOI: https://doi.org/10.1007/s10958-018-4125-1

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