Local free boundary problem for incompressible magnetohydrodynamics

Volume 509 / 2015

Piotr Kacprzyk Dissertationes Mathematicae 509 (2015), 1-52 MSC: Primary 35A01; Secondary 35Q30, 35R35, 76D05, 76W05. DOI: 10.4064/dm509-0-1


We consider the motion of an incompressible magnetohydrodynamic (mhd) fluid in a domain bounded by a free surface. In the external domain there exists an electromagnetic field generated by some currents which keeps the mhd flow in the bounded domain. Then on the free surface transmission conditions for electromagnetic fields are imposed. In this paper we prove 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.


  • Piotr KacprzykInstitute of Mathematics and Cryptology
    Cybernetics Faculty
    Military University of Technology
    Kaliskiego 2
    00-908 Warszawa, Poland

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