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Volume 12
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

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

by
Piotr Kacprzyk
1 and
Wojciech M. Zaja̧czkowski
1,2,*
1
Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, S. Kaliskiego 2, 00-908 Warsaw, Poland
2
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(17), 2614; https://doi.org/10.3390/math12172614
Submission received: 17 April 2024 / Revised: 3 June 2024 / Accepted: 21 June 2024 / Published: 23 August 2024
(This article belongs to the Special Issue Computational Fluid Dynamics with Applications)
Versions Notes

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 free boundary; incompressible; magnetohydrodynamics; transmission conditions; global existence

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MDPI and ACS Style

Kacprzyk, P.; Zaja̧czkowski, W.M. Global Existence of Solutions to a Free Boundary Problem for Viscous Incompressible Magnetohydrodynamics for Small Data. Mathematics 2024, 12, 2614. https://doi.org/10.3390/math12172614

AMA Style

Kacprzyk P, Zaja̧czkowski WM. Global Existence of Solutions to a Free Boundary Problem for Viscous Incompressible Magnetohydrodynamics for Small Data. Mathematics. 2024; 12(17):2614. https://doi.org/10.3390/math12172614

Chicago/Turabian Style

Kacprzyk, Piotr, and Wojciech M. Zaja̧czkowski. 2024. "Global Existence of Solutions to a Free Boundary Problem for Viscous Incompressible Magnetohydrodynamics for Small Data" Mathematics 12, no. 17: 2614. https://doi.org/10.3390/math12172614

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