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Volume 13
Issue 17
10.3390/math13172702
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

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

by
Wiesław J. Grygierzec
1 and
Wojciech M. Zaja̧czkowski
2,3,*
1
Department of Statistics and Social Policy, University of Agriculture in Kraków, Al. Mickiewicza 21, 31-120 Kraków, Poland
2
Institute of Mathematics (Emeritus Professor), Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland
3
Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, S. Kaliskiego 2, 00-908 Warsaw, Poland
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(17), 2702; https://doi.org/10.3390/math13172702
Submission received: 16 April 2025 / Revised: 16 July 2025 / Accepted: 28 July 2025 / Published: 22 August 2025
(This article belongs to the Special Issue Advances in Computational Dynamics and Mechanical Engineering)
Versions Notes

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.
Keywords: magnetohydrodynamics; compressible; free boundary; local existence magnetohydrodynamics; compressible; free boundary; local existence

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MDPI and ACS Style

Grygierzec, W.J.; Zaja̧czkowski, W.M. Existence of Local Solutions to a Free Boundary Problem for Compressible Viscous Magnetohydrodynamics. Mathematics 2025, 13, 2702. https://doi.org/10.3390/math13172702

AMA Style

Grygierzec WJ, Zaja̧czkowski WM. Existence of Local Solutions to a Free Boundary Problem for Compressible Viscous Magnetohydrodynamics. Mathematics. 2025; 13(17):2702. https://doi.org/10.3390/math13172702

Chicago/Turabian Style

Grygierzec, Wiesław J., and Wojciech M. Zaja̧czkowski. 2025. "Existence of Local Solutions to a Free Boundary Problem for Compressible Viscous Magnetohydrodynamics" Mathematics 13, no. 17: 2702. https://doi.org/10.3390/math13172702

APA Style

Grygierzec, W. J., & Zaja̧czkowski, W. M. (2025). Existence of Local Solutions to a Free Boundary Problem for Compressible Viscous Magnetohydrodynamics. Mathematics, 13(17), 2702. https://doi.org/10.3390/math13172702

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