We consider a motion of a viscous compressible heat conducting fluid of a fixed mass bounded by a free surface. For a local solution of equations describing such a motion we derive some energy-type inequalities which are necessary to prove the global existence of solutions.
In the paper the motion of a viscous compressible heat conducting capillary fluid in a domain bounded by a free surface is considered. We prove the local existence and uniqueness of a solution to a problem describing such a motion in anisotropic Sobolev-Slobodetskii spaces. This solution is such that the velocity and temperature belong to (wzór), and density to (wzór).
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