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Local free boundary problem for viscous compressible magnetohydrodynamics
Author(s) -
Kacprzyk Piotr
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5105
Subject(s) - magnetohydrodynamics , mathematics , bounded function , compressibility , domain (mathematical analysis) , free surface , mathematical analysis , viscous liquid , boundary (topology) , flow (mathematics) , surface (topology) , boundary value problem , electromagnetic field , compressible flow , classical mechanics , magnetic field , mechanics , physics , geometry , quantum mechanics
We consider the motion of viscous compressible magnetohydrodynamics fluid in a domain bounded by a free surface. In the external domain, there is electromagnetic field generated by some currents that keeps the magnetohydrodynamics flow in the bounded domain. Then on the free surface, transmission conditions for electromagnetic fields are imposed. In this paper, we prove the existence of local regular solutions by the method of successive approximations. The L 2 approach is used. This helps us to treat the transmission conditions.