On local motion of a general compressible viscous heat conducting fluid bounded by a free surface

• Autorzy: Ewa Zadrzyńska , Wojciech M. Zajączkowski
• Języki publikacji: EN

Abstrakty

EN

The motion of a viscous compressible heat conducting fluid in a domain in ℝ³ bounded by a free surface is considered. We prove local existence and uniqueness of solutions in Sobolev-Slobodetskiĭ spaces in two cases: with surface tension and without it.

Słowa kluczowe

EN

free boundary; compressible viscuous heat conducting fluid; local existence; anisotropic Sobolev spaces

Kategorie tematyczne

• 35R35: Free boundary problems
• 76N10: Existence, uniqueness, and regularity theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994
• Tom: 59
• Numer: 2
• Strony: 133-170

Daty

wydano

1994

otrzymano

1993-04-20

Twórcy

autor

Ewa Zadrzyńska

• Institute of Mathematics, Technical University of Łódź, Al. Politechniki 11, 90-924 Łódź, Poland

autor

Wojciech M. Zajączkowski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warsaw, Poland

Bibliografia

• [1] R. A. Adams, Sobolev Spaces, Academic Press, 1975.
• [2] G. Allain, Small-time existence for the Navier-Stokes equations with a free surface, Appl. Math. Optim. 16 (1987), 37-50.
• [3] O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, Integral Representations of Functions and Imbedding Theorems, Nauka, Moscow, 1975 (in Russian).
• [4] L. Landau and E. Lifschitz, Hydrodynamics, Nauka, Moscow, 1986 (in Russian).
• [5] T. Nishida, Equations of fluid dynamics: free surface problems, Comm. Pure Appl. Math. 39 (1986), 221-238.
• [6] P. Secchi and A. Valli, A free boundary problem for compressible viscous fluids, J. Reine Angew. Math. 341 (1983), 1-31.
• [7] V. A. Solonnikov, A priori estimates for parabolic equations of second order, Trudy Mat. Inst. Steklov. 70 (1964), 133-212 (in Russian).
• [8] V. A. Solonnikov, On boundary problems for linear parabolic systems of differential equations of general type, Trudy Mat. Inst. Steklov. 83 (1965) (in Russian); English transl.: Proc. Steklov Inst. Math. 83 (1967).
• [9] V. A. Solonnikov, On the solvability of the initial-boundary value problem for equations of motion of the viscous compressible fluid, Zap. Nauchn. Sem. LOMI 56 (1976), 128-142 (in Russian).
• [10] V. A. Solonnikov, On an unsteady motion of an isolated volume of a viscous incompressible fluid, Izv. Akad. Nauk SSSR Ser. Mat. 51 (5) (1987), 1065-1087 (in Russian).
• [11] V. A. Solonnikov, On an initial-boundary value problem for the Stokes system which appears in free boundary problems, Trudy Mat. Inst. Steklov. 188 (1990), 150-188 (in Russian).
• [12] V. Solonnikov and A. Tani, Free boundary problem for a viscous compressible flow with surface tension, in: Constantine Carathéodory: An International Tribute, T. M. Rassias (ed.), World Scientific, 1991, 1270-1303.
• [13] W. M. Zajączkowski, On local motion of a compressible barotropic viscous fluid bounded by a free surface, in: Partial Differential Equations, Banach Center Publ. 27, Inst. Math., Polish Acad. Sci., Warszawa, 1992, 511-553.
• [14] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993).
• [15] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous capillary fluid bounded by a free surface, to appear.
• [16] W. M. Zajączkowski, Local existence of solutions for free boundary problems for viscous fluids, to appear.