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

Ewa Zadrzyńska; Wojciech M. Zajączkowski

Annales Polonici Mathematici (1995)

- Volume: 61, Issue: 2, page 141-188
- ISSN: 0066-2216

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topEwa Zadrzyńska, and Wojciech M. Zajączkowski. "On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface." Annales Polonici Mathematici 61.2 (1995): 141-188. <http://eudml.org/doc/262296>.

@article{EwaZadrzyńska1995,

abstract = {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.},

author = {Ewa Zadrzyńska, Wojciech M. Zajączkowski},

journal = {Annales Polonici Mathematici},

keywords = {free boundary; compressible viscous heat conducting fluid; global differential inequality; free boundary problem for a viscous compressible heat conducting fluid},

language = {eng},

number = {2},

pages = {141-188},

title = {On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface},

url = {http://eudml.org/doc/262296},

volume = {61},

year = {1995},

}

TY - JOUR

AU - Ewa Zadrzyńska

AU - Wojciech M. Zajączkowski

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

JO - Annales Polonici Mathematici

PY - 1995

VL - 61

IS - 2

SP - 141

EP - 188

AB - 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.

LA - eng

KW - free boundary; compressible viscous heat conducting fluid; global differential inequality; free boundary problem for a viscous compressible heat conducting fluid

UR - http://eudml.org/doc/262296

ER -

## References

top- [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. Zbl0429.76040
- [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. Zbl0447.76053
- [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. Zbl0543.76099
- [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. Zbl0505.76083
- [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. Zbl0543.76099
- [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. Zbl0614.76026
- [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. Zbl0551.76022
- [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. Zbl0786.35106
- [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. Zbl0542.35062
- [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. Zbl0611.76082
- [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. Zbl0812.35102
- [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. Zbl0813.35130
- [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. Zbl0814.76075
- [18] E. Zadrzyńska and W. M. Zajączkowski, Conservation laws in free boundary problems for viscous compressible heat conducting capillary fluids, to appear. Zbl0880.76065
- [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. Zbl0885.35101
- [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. Zbl0874.35097
- [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. Zbl0874.35097
- [22] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993). Zbl0771.76059
- [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. Zbl0791.35105
- [24] W. M. Zajączkowski, Existence of local solutions for free boundary problems for viscous compressible barotropic fluids, Ann. Polon. Math. 60 (1995), 255-287. Zbl0923.35134
- [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. Zbl0813.35086

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