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1995 | 61 | 2 | 141-188
Tytuł artykułu

On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We derive a global differential inequality for solutions of a free boundary problem for a viscous compressible heat conducting fluid. The inequality is essential in proving the global existence of solutions.
Rocznik
Tom
61
Numer
2
Strony
141-188
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-11-03
poprawiono
1994-03-02
Twórcy
  • Institute of Mathematics and Operations Research, Military University of Technology, S. Kaliskiego 2, 01-489 Warszawa, Poland
  • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
Bibliografia
  • [1] O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, Integral Representation of Functions and Imbedding Theorems, Nauka, Moscow, 1975 (in Russian).
  • [2] L. Landau and E. Lifschitz, Mechanics of Continuum Media, Nauka, Moscow, 1984; new edition: Hydrodynamics, Nauka, Moscow, 1986 (in Russian).
  • [3] A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ. 20 (1980), 67-104.
  • [4] A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids, Proc. Japan Acad. Ser. A 55 (1979), 337-342.
  • [5] A. Matsumura and T. Nishida, The initial boundary value problem for the equations of motion of compressible viscous and heat-conductive fluids, preprint of Univ. of Wisconsin, MRC Technical Summary Report no. 2237, 1981.
  • [6] A. Matsumura and T. Nishida, Initial boundary value problems for the equations of motion of general fluids, in: Computing Methods in Applied Sciences and Engineering, V. R. Glovinski and J. L. Lions (eds.), North-Holland, Amsterdam, 1982.
  • [7] A. Matsumura and T. Nishida, Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids, Comm. Math. Phys. 89 (1983), 445-464.
  • [8] K. Pileckas and W. M. Zajączkowski, On the boundary problem for stationary compressible Navier-Stokes equations, Comm. Math. Phys. 128 (1990), 1-36.
  • [9] V. A. Solonnikov, On an unsteady flow of a finite mass of a liquid bounded by a free surface, Zap. Nauchn. Sem. LOMI 152 (1986), 137-157 (in Russian); English transl.: J. Soviet Math. 10 (1988), 672-686.
  • [10] V. A. Solonnikov, Solvability of the evolution problem for an isolated mass of a viscous incompressible capillary liquid, Zap. Nauchn. Sem. LOMI 140 (1984), 179-186 (in Russian); English transl.: J. Soviet Math. 33 (1986), 223-238.
  • [11] V. A. Solonnikov, On unsteady motion of an isolated volume of a viscous incompressible fluid, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987), 1065-1087 (in Russian).
  • [12] V. A. Solonnikov and A. Tani, Evolution free boundary problem for equations of motion of viscous compressible barotropic liquids, preprint of Paderborn University.
  • [13] A. Valli, Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method, Ann. Scuola Norm. Sup. Pisa (4) 10 (1983), 607-647.
  • [14] A. Valli and W. M. Zajączkowski, Navier-Stokes equations for compressible fluids: global existence and qualitative properties of the solution in the general case, Comm. Math. Phys. 103 (1986), 259-296.
  • [15] E. Zadrzyńska and W. M. Zajączkowski, On local motion of a general compressible viscous heat conducting fluid bounded by a free surface, Ann. Polon. Math. 59 (1994), 133-170.
  • [16] E. Zadrzyńska and W. M. Zajączkowski, On global motion of a compressible heat conducting fluid bounded by a free surface, Acta Appl. Math., to appear.
  • [17] E. Zadrzyńska and W. M. Zajączkowski, Conservation laws in free boundary problems for viscous compressible heat conducting fluids, Bull. Polish Acad. Sci. Tech. Sci. 42 (1994), 197-207.
  • [18] E. Zadrzyńska and W. M. Zajączkowski, Conservation laws in free boundary problems for viscous compressible heat conducting capillary fluids, to appear.
  • [19] E. Zadrzyńska and W. M. Zajączkowski, On a differential inequality for equations of a viscous compressible heat conducting capillary fluid bounded by a free surface, to appear.
  • [20] E. Zadrzyńska and W. M. Zajączkowski, On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid, Inst. Math., Pol. Acad. Sci., Prepr. 523 (1994), 1-22.
  • [21] E. Zadrzyńska and W. M. Zajączkowski, On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting capillary fluid, to appear.
  • [22] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993).
  • [23] W. M. Zajączkowski, On local motion of a compressible viscous fluid bounded by a free surface, in: Partial Differential Equations, Banach Center Publ. 27, Inst. Math., Polish Acad. Sci., Warszawa, 1992, 511-553.
  • [24] W. M. Zajączkowski, Existence of local solutions for free boundary problems for viscous compressible barotropic fluids, Ann. Polon. Math. 60 (1995), 255-287.
  • [25] W. M. Zajączkowski, On Nonstationary Motion of A Compressible Barotropic Viscous Capillary Fluid Bounded By A Free Surface, Siam J. Math. Anal. 25 (1994), 1-84.
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Bibliografia
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