We derive an inequality for a local solution of a free boundary problem for a viscous compressible heat-conducting capillary fluid. This inequality is crucial to proving the global existence of solutions belonging to certain anisotropic Sobolev-Slobodetskiĭ spaces and close to an equilibrium state.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am29-4-3, author = {Ewa Zadrzy\'nska and Wojciech M. Zaj\k aczkowski}, title = {On an inequality for a free boundary problem for equations of a viscous compressible heat-conducting capillary fluid}, journal = {Applicationes Mathematicae}, volume = {29}, year = {2002}, pages = {399-438}, zbl = {1010.35084}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-4-3} }
Ewa Zadrzyńska; Wojciech M. Zajączkowski. On an inequality for a free boundary problem for equations of a viscous compressible heat-conducting capillary fluid. Applicationes Mathematicae, Tome 29 (2002) pp. 399-438. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-4-3/