The local existence and the uniqueness of solutions for equations describing the motion of viscous compressible heat-conducting fluids in a domain bounded by a free surface is proved. First, we prove the existence of solutions of some auxiliary problems by the Galerkin method and by regularization techniques. Next, we use the method of successive approximations to prove the local existence for the main problem.
@article{bwmeta1.element.bwnjournal-article-zmv25i2p179bwm,
author = {Ewa Zadrzy\'nska and Wojciech Zaj\k aczkowski},
title = {Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids},
journal = {Applicationes Mathematicae},
volume = {25},
year = {1998},
pages = {179-220},
zbl = {0906.35079},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i2p179bwm}
}
Zadrzyńska, Ewa; Zajączkowski, Wojciech. Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids. Applicationes Mathematicae, Tome 25 (1998) pp. 179-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i2p179bwm/
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