Almost global solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid
Volume 31 / 2004
Applicationes Mathematicae 31 (2004), 69-77
MSC: 35A05, 35R35, 76N10.
DOI: 10.4064/am31-1-6
Abstract
Almost global in time existence of solutions for equations describing the motion of a magnetohydrodynamic incompressible fluid in a domain bounded by a free surfaced is proved. In the exterior domain we have an electromagnetic field which is generated by some currents which are located on a fixed boundary. We prove that a solution exists for $t\in (0,T)$, where $T>0$ is large if the data are small.
