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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- 6.O. A. Ladyzhenskaya, “On the unique solvability in large of a three-dimensional Cauchy problem for the Navier–Stokes equations in the presence of axial symmetry,” Zap. Nauchn. Semin. LOMI, 7, 155–177 (1968).Google Scholar
- 10.S. Leonardi, J. Malek, J. Necas, and M. Pokorny, “On axially symmetric flows in ℝ3,” Z. Anal. Anwendungen, 18, No. 3, 639–649.Google Scholar
- 12.B. Nowakowski and W. Zajaczkowski, “On global regular solutions to magnetohydrodynamics in axi-symmetric domains,” Z. Angew. Math. Phys., 67, No. 6, Art. 142 (2016).Google Scholar