Displaying similar documents to “A free boundary problem describing the saturated-unsaturated flow in a porous medium. II: Existence of the free boundary in the 3D case.”

On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface

Wojciech M. Zajączkowski

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We consider the motion of a viscous compressible barotropic fluid in ℝ 3 bounded by a free surface which is under constant exterior pressure. For a given initial density, initial domain and initial velocity we prove the existence of local-in-time highly regular solutions. Next assuming that the initial density is sufficiently close to a constant, the initial pressure is sufficiently close to the external pressure, the initial velocity is sufficiently small and the external force vanishes...

On local motion of a compressible barotropic viscous fluid bounded by a free surface

W. Zajączkowski (1992)

Banach Center Publications

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We consider the motion of a viscous compressible barotropic fluid in ℝ³ bounded by a free surface which is under constant exterior pressure, both with surface tension and without it. In the first case we prove local existence of solutions in anisotropic Hilbert spaces with noninteger derivatives. In the case without surface tension the anisotropic Sobolev spaces with integration exponent p > 3 are used to omit the coefficients which are increasing functions of 1/T, where T is the...