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

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 electro...

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Bibliographic Details
Published inMathematics (Basel) Vol. 12; no. 17; p. 2614
Main Authors Kacprzyk, Piotr, Zaja̧czkowski, Wojciech M.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2024
Subjects
Boundary conditions
Charged particles
Electric fields
Electromagnetic fields
Electromagnetism
Estimates
Free boundaries
free boundary
Free surfaces
global existence
incompressible
Inequality
Magnetic fields
Magnetohydrodynamics
transmission conditions
Velocity
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12172614