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1998-1999 | 25 | 4 | 489-511
Tytuł artykułu

On nonstationary motion of a fixed mass of a general viscous compressible heat conducting capillary fluid bounded by a free boundary

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The motion of a fixed mass of a viscous compressible heat conducting capillary fluid is examined. Assuming that the initial data are sufficiently close to a constant state and the external force vanishes we prove the existence of a global-in-time solution which is close to the constant state for any moment of time. Moreover, we present an analogous result for the case of a barotropic viscous compressible fluid.
Rocznik
Tom
25
Numer
4
Strony
489-511
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-06-30
Twórcy
  • Institute of Mathematics and Operations Research, Military University of Technology, S. Kaliskiego 2, 01-489 Warszawa, Poland
Bibliografia
  • [1] 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).
  • [2] 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.
  • [3] 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.
  • [4] 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).
  • [5] 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.
  • [6] A. Matsumura and T. Nishida, Initial boundary value problems for the equations of motion of compressible and heat-conductive fluids, Comm. Math. Phys. 89 (1983), 445-464.
  • [7] V. A. 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 Sci., 1991, 1270-1303.
  • [8] V. A. Solonnikov and A. Tani, Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid, preprint, Paderborn University.
  • [9] G. Ströhmer and W. M. Zajączkowski, Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids, Appl. Math. (Warsaw), to appear.
  • [10] G. Ströhmer and W. M. Zajączkowski, On the existence and properties of the rotationally symmetric equilibrium states of compressible barotropic selt-gravitating fluids, Indiana Univ. Math. J. 46 (1997), 1181-1220.
  • [11] G. Ströhmer and W. M. Zajączkowski, On stability of equilibrium solution for compressible barotropic viscous self-gravitating fluid motions bounded by a free surface, to appear.
  • [12] 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.
  • [13] 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.
  • [14] 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.
  • [15] E. Zadrzyńska and W. M. Zajączkowski, Conservation laws in free boundary problems for viscous compressible heat conducting capillary fluids, ibid. 43 (1995), 423-444.
  • [16] E. Zadrzyńska and W. M. Zajączkowski On a differential inequality for a viscous compressible heat conducting fluid bounded by a free surface, Ann. Polon. Math. 61 (1995), 141-188.
  • [17] E. Zadrzyńska and W. M. Zajączkowski On a differential inequality for a viscous compressible heat conducting fluid bounded by a free surface, On a differential inequality for a viscous compressible heat conducting capillary fluid bounded by a free surface, ibid. 65 (1996), 23-53.
  • [18] E. Zadrzyńska and W. M. Zajączkowski On a differential inequality for a viscous compressible heat conducting fluid bounded by a free surface, On the global existence theorem for a free boundary problem for a viscous compressible heat conducting fluid, ibid. 63 (1996), 199-221.
  • [19] E. Zadrzyńska and W. M. Zajączkowski On a differential inequality for a viscous compressible heat conducting fluid bounded by a free surface, On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting capillary fluid, J. Appl. Anal. 2 (1996), 125-169.
  • [20] E. Zadrzyńska and W. M. Zajączkowski On a differential inequality for a viscous compressible heat conducting fluid bounded by a free surface, Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids, Appl. Math. (Warsaw) 25 (1998), 179-220.
  • [21] E. Zadrzyńska and W. M. Zajączkowski On a differential inequality for a viscous compressible heat conducting fluid bounded by a free surface, On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary, Colloq. Math. 79 (1999), 283-310.
  • [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 nonstationary motion of a compressible barotropic viscous capillary fluid bounded by a free surface, SIAM J. Math. Anal. 25 (1994), 1-84.
  • [24] W. M. Zajączkowski, Existence of local solutions for free boundary problems for viscous compressible barotropic fluids, Ann. Polon. Math. 60 (1995), 255-287.
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