Displaying similar documents to “On some inequalities for solutions of equations describing the motion of a viscous compressible heat-conducting capillary fluid bounded by a free surface”

On an inequality for a free boundary problem for equations of a viscous compressible heat-conducting capillary fluid

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2002)

Applicationes Mathematicae

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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.

On nonstationary motion of a fixed mass of a general fluid bounded by a free surface

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2003)

Banach Center Publications

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In the paper the motion of a fixed mass of a viscous compressible heat conducting fluid is considered. Assuming that the initial data are sufficiently close to an equilibrium state and the external force, the heat sources and the heat flow through the boundary vanish, we prove the existence of a global in time solution which is close to the equilibrium state for any moment of time.