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.
@article{bwmeta1.element.bwnjournal-article-apmv61z2p141bwm,
author = {Ewa Zadrzy\'nska and Wojciech M. Zaj\k aczkowski},
title = {On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {141-188},
zbl = {0833.35156},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv61z2p141bwm}
}
Ewa Zadrzyńska; Wojciech M. Zajączkowski. On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface. Annales Polonici Mathematici, Tome 62 (1995) pp. 141-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv61z2p141bwm/
[000] [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).
[001] [2] L. Landau and E. Lifschitz, Mechanics of Continuum Media, Nauka, Moscow, 1984; new edition: Hydrodynamics, Nauka, Moscow, 1986 (in Russian).
[002] [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. | Zbl 0429.76040
[003] [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. | Zbl 0447.76053
[004] [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. | Zbl 0543.76099
[005] [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. | Zbl 0505.76083
[006] [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. | Zbl 0543.76099
[007] [8] K. Pileckas and W. M. Zajączkowski, On the boundary problem for stationary compressible Navier-Stokes equations, Comm. Math. Phys. 128 (1990), 1-36.
[008] [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. | Zbl 0614.76026
[009] [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. | Zbl 0551.76022
[010] [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).
[011] [12] V. A. Solonnikov and A. Tani, Evolution free boundary problem for equations of motion of viscous compressible barotropic liquids, preprint of Paderborn University. | Zbl 0786.35106
[012] [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. | Zbl 0542.35062
[013] [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. | Zbl 0611.76082
[014] [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. | Zbl 0812.35102
[015] [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. | Zbl 0813.35130
[016] [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. | Zbl 0814.76075
[017] [18] E. Zadrzyńska and W. M. Zajączkowski, Conservation laws in free boundary problems for viscous compressible heat conducting capillary fluids, to appear. | Zbl 0880.76065
[018] [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. | Zbl 0885.35101
[019] [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. | Zbl 0874.35097
[020] [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. | Zbl 0874.35097
[021] [22] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993). | Zbl 0771.76059
[022] [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. | Zbl 0791.35105
[023] [24] W. M. Zajączkowski, Existence of local solutions for free boundary problems for viscous compressible barotropic fluids, Ann. Polon. Math. 60 (1995), 255-287. | Zbl 0923.35134
[024] [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. | Zbl 0813.35086