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

We consider the motion of an incompressible magnetohydrodynamics with resistivity in a domain bounded by a free surface which is coupled through the free surface with an electromagnetic field generated by a magnetic field prescribed on an exterior fixed boundary. On the free surface, transmission co...

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Bibliographic Details
Published inJournal of mathematical fluid mechanics Vol. 26; no. 3
Main Authors Kacprzyk, Piotr, Zaja̧czkowski, Wojciech M.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2024
Springer Nature B.V
Subjects
Classical and Continuum Physics
Electric fields
Electromagnetic fields
Fluid- and Aerodynamics
Free boundaries
Free surfaces
Magnetic fields
Magnetohydrodynamics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Transmission conditions on the free surface
Free boundary
Secondary 35Q30
The method of successive approximations
35R35
Primary 35A01
Regularizer technique
Incompressible magnetohydrodynamics with resistivity
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Summary:We consider the motion of an incompressible magnetohydrodynamics with resistivity in a domain bounded by a free surface which is coupled through the free surface with an electromagnetic field generated by a magnetic field prescribed on an exterior fixed boundary. On the free surface, transmission conditions for the electromagnetic field are imposed. As transmission condition we assume jumps of tangent components of magnetic and electric fields on the free surface. We prove local existence of solutions such that velocity and magnetic fields belong to H 2 + α , 1 + α / 2 , α > 5 / 8 .
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-024-00879-y