## Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic compressible fluid

### Volume 31 / 2004

Applicationes Mathematicae 31 (2004), 209-227
MSC: 35A05, 35R35, 76N10.
DOI: 10.4064/am31-2-6

#### Abstract

Local existence of solutions for the equations describing the motion of a magnetohydrodynamic compressible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linearized equations is proved, next by the method of successive aproximations local existence to the nonlinear problem is shown.