Global free boundary problem for incompressible magnetohydrodynamics
Volume 510 / 2015
Dissertationes Mathematicae 510 (2015), 1-44
MSC: Primary 35A01; Secondary 35Q30, 35R35, 76D05, 76W05.
DOI: 10.4064/dm510-0-1
Abstract
We consider the motion of incompressible mhd in a domain bounded 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. On the free surface transmission conditions for the electromagnetic fields are imposed. For sufficiently small initial velocity and vanishing external force the global existence is proved. The $L_2$-approach is used. This helps us to treat the transmission conditions.
