JournalsifbVol. 14, No. 4pp. 569–602

Free boundary problems of magnetohydrodynamics in multi-connected domains

  • Vsevolod A. Solonnikov

    Russian Acadademy of Sciences, St. Petersburg, Russian Federation
Free boundary problems of magnetohydrodynamics in multi-connected domains cover
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Abstract

The subject of the paper is the solvability theory of evolution free boundary problems of magnetohydrodynamics for viscous incompressible liquid in multi-connected domains. The main result is the local existence theorem for such problems under rather general assumptions on the initial data of the problem, i.e., on the initial configuration of the liquid and on the initial values of the velocity vector field vv and of the magnetic field HH. The solution is found in anisotropic Sobolev–Slobodetskii spaces.

Cite this article

Vsevolod A. Solonnikov, Free boundary problems of magnetohydrodynamics in multi-connected domains. Interfaces Free Bound. 14 (2012), no. 4, pp. 569–602

DOI 10.4171/IFB/292