On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid
Tom 63 / 1996
Annales Polonici Mathematici 63 (1996), 199-221 DOI: 10.4064/ap-63-3-199-221
We consider the motion of a viscous compressible heat conducting fluid in ℝ³ bounded by a free surface which is under constant exterior pressure. Assuming that the initial velocity is sufficiently small, the initial density and the initial temperature are close to constants, the external force, the heat sources and the heat flow vanish, we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.