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

Volume 27 / 1992

W. Zajączkowski Banach Center Publications 27 (1992), 511-553 DOI: 10.4064/-27-2-511-553


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 existence time.


  • W. Zajączkowski

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