We prove the local existence of solutions for equations of motion of a viscous compressible barotropic fluid in a domain bounded by a free surface. The solutions are shown to exist in exactly those function spaces where global solutions were found in our previous papers [14, 15].
@article{bwmeta1.element.bwnjournal-article-apmv60z3p255bwm,
author = {W. M. Zaj\k aczkowski},
title = {Existence of local solutions for free boundary problems for viscous compressible barotropic fluids},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {255-287},
zbl = {0923.35134},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv60z3p255bwm}
}
W. M. Zajączkowski. Existence of local solutions for free boundary problems for viscous compressible barotropic fluids. Annales Polonici Mathematici, Tome 62 (1995) pp. 255-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv60z3p255bwm/
[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] D. K. Faddeev, V. A. Solonnikov and N. N. Ural'tseva, Selected Topics of Analysis and Algebra, Leningrad, 1981 (in Russian).
[002] [3] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967 (in Russian).
[003] [4] L. Landau and E. Lifschitz, Mechanics of Continuum Media, Nauka, Moscow, 1954 (in Russian); English transl.: Pergamon Press, Oxford, 1959; new edition: Hydrodynamics, Nauka, Moscow, 1986 (in Russian).
[004] [5] V. A. Solonnikov, On an initial-boundary value problem for the Stokes system which appears in free boundary problems, Trudy Mat. Inst. Steklov. 188 (1990), 150-188 (in Russian).
[005] [6] V. A. Solonnikov, On boundary problems for linear parabolic systems of differential equations of general form, ibid. 83 (1965) (in Russian). | Zbl 0164.12502
[006] [7] V. A. Solonnikov, A priori estimates for second order parabolic equations, ibid. 70 (1964), 133-212 (in Russian). | Zbl 0168.08202
[007] [8] V. A. Solonnikov and A. Tani, Free boundary problem for a viscous compressible flow with a surface tension, in: Constantine Carathéeodory: An International Tribute, T. M. Rassias (ed.), World Scientific, 1991, 1270-1303. | Zbl 0752.35096
[008] [9] 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
[009] [10] 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, to appear. | Zbl 0874.35097
[010] [11] 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
[011] [12] W. M. Zajączkowski, On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations, Dissertationes Math. 304 (1990).
[012] [13] W. M. Zajączkowski, On local motion of a compressible barotropic viscous fluid bounded by a free surface, in: Banach Center Publ. 27, Inst. Math., Polish Acad. Sci., 1992, 511-553. | Zbl 0791.35105
[013] [14] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993). | Zbl 0771.76059
[014] [15] 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