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Journal of Mathematical Sciences

, Volume 195, Issue 1, pp 76–97 | Cite as

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

  • V. A. Solonnikov
  • E. V. Frolova
Article

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.

Keywords

Initial Data Initial Position Free Boundary Boundary Problem Free Boundary Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.St. Petersburg State Electrotechnical University, St. Petersburg State UniversitySt. PetersburgRussia

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