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Existence of Local Solutions to a Free Boundary Problem for Compressible Viscous Magnetohydrodynamics

Author

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  • Wiesław J. Grygierzec

    (Department of Statistics and Social Policy, University of Agriculture in Kraków, Al. Mickiewicza 21, 31-120 Kraków, Poland)

  • Wojciech M. Zaja̧czkowski

    (Institute of Mathematics (Emeritus Professor), Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland
    Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, S. Kaliskiego 2, 00-908 Warsaw, Poland)

Abstract

The motion of viscous compressible magnetohydrodynamics (MHD) is considered in a domain bounded by a free boundary. The motion interacts through the free surface with an electromagnetic field located in a domain that is exterior to the free surface and bounded by a given fixed surface. Some data for the electromagnetic fields are prescribed on this fixed boundary. On the free surface, jumps in magnetic and electric fields are assumed. We prove the local existence of solutions by the method of successive approximations using Sobolev–Slobodetskii spaces.

Suggested Citation

  • Wiesław J. Grygierzec & Wojciech M. Zaja̧czkowski, 2025. "Existence of Local Solutions to a Free Boundary Problem for Compressible Viscous Magnetohydrodynamics," Mathematics, MDPI, vol. 13(17), pages 1-47, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2702-:d:1730296
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