Local free boundary problem for incompressible magnetohydrodynamics
Tom 509 / 2015
Dissertationes Mathematicae 509 (2015), 1-52
MSC: Primary 35A01; Secondary 35Q30, 35R35, 76D05, 76W05.
DOI: 10.4064/dm509-0-1
Streszczenie
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.
