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Solvability of a free boundary problem of magnetohydrodynamics in an infinite time interval

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The global in time solvability of a free boundary problem governing the motion of finite isolated mass of a viscous incompressible electrically conducting capillary liquid in vacuum is proved under smallness assumptions on the initial data. The initial position of the free boundary is assumed to be close to a sphere. It is shown that if t→∞, then the solution tends to zero exponentially and the free boundary tends to a sphere of the same radius, but, in general, the sphere may have a different center. The solution is obtained in the Sobolev--lobodetskii spaces \( W_2^{2+l,1+l/2 },1/2<l<1 \). Bibliography: 14 titles.

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Authors and Affiliations

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

    V. A. Solonnikov

  2. St. Petersburg State Electrotechnical University, St. Petersburg State University, St. Petersburg, Russia

    E. V. Frolova

Authors
  1. V. A. Solonnikov
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  2. E. V. Frolova
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Correspondence to V. A. Solonnikov.

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Dedicated to the memory of Professor M. Padula

Published in Zapiski Nauchnyk Seminarov POMI, Vol. 410, 2013, pp. 131–167.

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Solonnikov, V.A., Frolova, E.V. Solvability of a free boundary problem of magnetohydrodynamics in an infinite time interval. J Math Sci 195, 76–97 (2013). https://doi.org/10.1007/s10958-013-1565-5

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  • DOI: https://doi.org/10.1007/s10958-013-1565-5

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