Differential inequalities for general fluid motions bounded by a free surface

• Autorzy: Zadrzyńska E. , Zajączkowski W. M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

free boundary; compressible viscous heat conducting fluid

PL

wolny brzeg(granica); ściśliwe lepkie ciecze przewodzące ciepło

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2004
• Tom: Vol. 10, nr 1
• Strony: 131--168
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Zadrzyńska E.

• Faculty of Mathematics and Information Sciences Warsaw University of Technology Pl. Politechniki 1 00-661 Warsaw, Poland

autor

Zajączkowski W. M.

• Interdisciplinary Centre for Mathematical and Computational Modeling, Warsaw University, Pawińskiego 5A, 02-106 Warsaw, Poland

Bibliografia

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• [2] Ladyzhenskaya, O. A., Solonnikov, V. A., On some problems of vector analysis and generalized formulations of boundary problems for Navier-Stokes equations, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 59 (1976), 81-116 (in Russian).
• [3] Landau, L., Lifschitz, E., Hydrodynamics, Nauka, Moscow, 1986 (in Russian).
• [4] Serrin, J., Mathematical principles of classical fluid mechanics, in “Handbuch der Physik”, Bd. VIII/1, Springer, Berlin, Göttingen, Heidelberg, 1959.
• [5] Zadrzyńska, E., On nonstationary motion of a fixed mass of a general viscous compressible heat conducting capillary fluid bounded by a free boundary, Appl. Math. 25 (1999), 489-511.
• [6] Zadrzyńska, E., Zajączkowski, W. M., On differential inequality for equations of a viscous compressible heat-conducting fluid bounded by a free surface, Ann. Polon. Math. 61 (1995), 141-188.
• [7] Zadrzyńska, E., Zajączkowski, W. M., On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid, Ann. Polon. Math. 63 (1996), 199-221.
• [8] Zadrzyńska, E., Zajączkowski, W. M., Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids, Appl. Math. 25 (1998), 179-200.
• [9] Zadrzyńska, E., Zajączkowski, W. M., On nonstationary motion of a fixed mass of a general fluid bounded by a free surface, Banach Center Publ. 60 (2003), 253-266.
• [10] Zajączkowski, W. M., On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993).
• [11] Zajączkowski, W. M., On nonstationary motion of a compressible barotropic viscous capillary fluid bounded by a free surface, SIAM J. Math. Anal. 25 (1994), 1-84.