Global Existence of Solutions to a Free Boundary Problem for Viscous Incompressible Magnetohydrodynamics for Small Data

Piotr Kacprzyk and Wojciech M. Zaja̧czkowski ()
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Piotr Kacprzyk: Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, S. Kaliskiego 2, 00-908 Warsaw, Poland
Wojciech M. Zaja̧czkowski: Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, S. Kaliskiego 2, 00-908 Warsaw, Poland

Mathematics, 2024, vol. 12, issue 17, 1-58

Abstract: The motion of viscous incompressible magnetohydrodynamics (MHD) is considered in a domain that is bounded by a free surface. The motion interacts through the free surface with an electromagnetic field located in a domain exterior to the free surface and bounded by a given fixed surface. Some electromagnetic fields are prescribed on this fixed boundary. On the free surface, jumps in the magnetic and electric fields are assumed. The global existence of solutions to this problem assuming appropriate smallness conditions on the initial and boundary data is proved.

Keywords: free boundary; incompressible; magnetohydrodynamics; transmission conditions; global existence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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