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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-8,
author = {Piotr Kacprzyk},
title = {Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid},
journal = {Applicationes Mathematicae},
volume = {30},
year = {2003},
pages = {461-488},
zbl = {1059.35106},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-8}
}
Piotr Kacprzyk. Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid. Applicationes Mathematicae, Tome 30 (2003) pp. 461-488. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-8/