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1996-1997 | 65 | 1 | 23-53
Tytuł artykułu

On a differential inequality for a viscous compressible heat conducting capillary 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 concluding capillary fluid. The inequality is essential in proving the global existence of solutions.
Rocznik
Tom
65
Numer
1
Strony
23-53
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-12-19
Twórcy
  • Department of Mathematics, 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 Representations 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 fluid, preprint Univ. of Wisconsin, MRC Technical Summary Report 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, R. Glowinski and J. L. Lions (eds.), North-Holland, Amsterdam, 1982, 389-406.
  • [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 free boundary problem for stationary compressible Navier-Stokes equations, Comm. Math. Phys. 128 (1990), 1-36.
  • [9] V. A. Solonnikov and A. Tani, Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid, preprint of Paderborn University.
  • [10] 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.
  • [11] 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.
  • [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 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), 195-205.
  • [15] E. Zadrzyńska and W. M. Zajączkowski, Conservation laws in free boundary problems for viscous compressible heat conducting capillary fluids, Bull. Polish Acad. Sci. Tech. Sci. 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 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.
  • [18] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993).
  • [19] 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.
Typ dokumentu
Bibliografia
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