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1996 | 63 | 3 | 199-221
Tytuł artykułu

On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the motion of a viscous compressible heat conducting fluid in ℝ³ bounded by a free surface which is under constant exterior pressure. Assuming that the initial velocity is sufficiently small, the initial density and the initial temperature are close to constants, the external force, the heat sources and the heat flow vanish, we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.
Rocznik
Tom
63
Numer
3
Strony
199-221
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-03-21
poprawiono
1994-12-10
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] J. T. Beale, The initial value problem for the Navier-Stokes equations with a free boundary, Comm. Pure Appl. Math. 31 (1980), 359-392.
  • [2] J. T. Beale, Large time regularity of viscous surface waves, Arch. Rational Mech. Anal. 84 (1984), 307-352.
  • [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); English transl.: Scripta Series in Mathematics, Winston and Halsted Press, 1979.
  • [4] L. Landau and E. Lifschitz, Mechanics of Continuum Media, Nauka, Moscow, 1984 (in Russian); English transl.: Pergamon Press, Oxford, 1959; new edition: Hydrodynamics, Nauka, Moscow, 1986 (in Russian).
  • [5] 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.
  • [6] 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.
  • [7] A. Matsumura and T. Nishida, The initial boundary value problem for the equations of motion of compressible viscous and heat-conductive fluid, preprint of Univ. of Wisconsin, MRC Technical Summary Report no. 2237 (1981).
  • [8] 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, R. Glowinski and J. L. Lions (eds.), North-Holland, Amsterdam, 1982, 389-406.
  • [9] 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.
  • [10] V. A. Solonnikov, A priori estimates for parabolic equations of second order, Trudy Mat. Inst. Steklov 70 (1964), 133-212 (in Russian).
  • [11] 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. 40 (1988), 672-686.
  • [12] 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. 32 (1986), 223-238.
  • [13] V. A. Solonnikov, On an unsteady motion of an isolated volume of a viscous incompressible fluid, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987), 1065-1087 (in Russian).
  • [14] V. A. Solonnikov and A. Tani, Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid, preprint of Paderborn University.
  • [15] A. Valli and W. M. Zajączkowski, Navier-Stokes equations for compressible fluids: global existence and qualitative properties of the solutions in the general case, Comm. Math. Phys. 103 (1986), 259-296.
  • [16] 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.
  • [17] E. Zadrzyńska and W. M. Zajączkowski, On global motion of a compressible viscous heat conducting fluid bounded by a free surface, Acta Appl. Math. 37 (1994), 221-231.
  • [18] 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.
  • [19] E. Zadrzyńska and W. M. Zajączkowski, On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface, Ann. Polon. Math. 61 (1995), 141-188.
  • [20] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993).
  • [21] 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, Part 2, Inst. Math., Polish Acad. Sci., 1992, 511-553.
  • [22] W. M. Zajączkowski, Existence of local solutions for free boundary problems for viscous compressible barotropic fluids, Ann. Polon. Math. 60 (1995), 255-287.
  • [23] 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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