Email this article On the Local Smoothness of Some Class of Axially-Symmetric Solutions to the MHD Equations
- Authors: Shilkin T.1
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Affiliations:
- St. Petersburg Department of the Steklov Mathematical Institute
- Issue: Vol 236, No 4 (2019)
- Pages: 461-475
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/242247
- DOI: https://doi.org/10.1007/s10958-018-4125-1
- ID: 242247
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Abstract
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.
About the authors
T. Shilkin
St. Petersburg Department of the Steklov Mathematical Institute
Author for correspondence.
Email: shilkin@pdmi.ras.ru
Russian Federation, St. Petersburg
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