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

### Volume 30 / 2003

Applicationes Mathematicae 30 (2003), 461-488
MSC: 35A05, 35R35, 76N10.
DOI: 10.4064/am30-4-8

#### Abstract

Local existence of solutions is proved for equations describing the motion of a magnetohydrodynamic incompressible fluid in a domain bounded by a free surface. 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 linarized equations is proved; next by the method of successive aproximations the local existence is shown for the nonlinear problem.