On local motion of a general compressible viscous heat conducting fluid bounded by a free surface

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1. [1] R. A. Adams, Sobolev Spaces, Academic Press, 1975. 
2. [2] G. Allain, Small-time existence for the Navier-Stokes equations with a free surface, Appl. Math. Optim. 16 (1987), 37-50. 
3. [3] O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, Integral Representations of Functions and Imbedding Theorems, Nauka, Moscow, 1975 (in Russian). 
4. [4] L. Landau and E. Lifschitz, Hydrodynamics, Nauka, Moscow, 1986 (in Russian). 
5. [5] T. Nishida, Equations of fluid dynamics: free surface problems, Comm. Pure Appl. Math. 39 (1986), 221-238. 
6. [6] P. Secchi and A. Valli, A free boundary problem for compressible viscous fluids, J. Reine Angew. Math. 341 (1983), 1-31. Zbl0502.76082
7. [7] V. A. Solonnikov, A priori estimates for parabolic equations of second order, Trudy Mat. Inst. Steklov. 70 (1964), 133-212 (in Russian). 
8. [8] V. A. Solonnikov, On boundary problems for linear parabolic systems of differential equations of general type, Trudy Mat. Inst. Steklov. 83 (1965) (in Russian); English transl.: Proc. Steklov Inst. Math. 83 (1967). Zbl0164.12502
9. [9] V. A. Solonnikov, On the solvability of the initial-boundary value problem for equations of motion of the viscous compressible fluid, Zap. Nauchn. Sem. LOMI 56 (1976), 128-142 (in Russian). Zbl0338.35078
10. [10] V. A. Solonnikov, On an unsteady motion of an isolated volume of a viscous incompressible fluid, Izv. Akad. Nauk SSSR Ser. Mat. 51 (5) (1987), 1065-1087 (in Russian). 
11. [11] 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). 
12. [12] V. 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 Scientific, 1991, 1270-1303. Zbl0752.35096
13. [13] W. M. Zajączkowski, On local motion of a compressible barotropic 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
14. [14] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993). Zbl0771.76059
15. [15] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous capillary fluid bounded by a free surface, to appear. Zbl0813.35086
16. [16] W. M. Zajączkowski, Local existence of solutions for free boundary problems for viscous fluids, to appear. 

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