On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting capillary fluid

E. Zadrzynska and W.M. Zajaczkowski

Abstract: We consider the motion of a viscous compressible heat conducting fluid in ${\Bbb R}^3$ bounded by a free surface which is under surface tension and 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.

Keywords: Viscous compressible heat conducting fluid, global existence, freeboundary problem, surface tension

Classification (MSC2000): 35A05, 35R35, 76N10

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