LIU Jian . LOCAL EXISTENCE OF SOLUTION TO FREE BOUNDARY VALUE PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1298 -1320 . DOI: 10.1016/S0252-9602(12)60100-3

[1] Bresch D, Desjardins B. Some diffusive capillary models for Korteweg type. C R Mecanique, 2004, 332(11): 881–886

[2] Chen P, Fang D, Zhang T. Free boundary problem for compressible flows with density-dependent viscosity coefficients. Commun Pure Appl Anal, 2011, 10: 459–478

[3] Chen P, Zhang T. A vacuum problem for multidimensional compressible Navier-Stokes equations with degenerate viscosity coefficients. Commun Pure Appl Anal, 2008, 7: 987–1016

[4] Fang D, Zhang T. Compressible Navier-Stokes equations with vacuum state in the case of general pressure law. Math Methods Appl Sci, 2006, 29: 1081–1106

[5] Hoff D, Serre D. The failure of continuous dependence on initial data for the Navier-Stokes equations of compressible flow. SIAM J Appl Math, 1991, 51: 887–898

[6] Huang F M, Wang Y, Zhai X Y. Stability of viscous contact wave for compressible Navier-Stokes system of general gas with free boundary. Acta Math Sci, 2010, 30B(6): 1906–1916

[7] Gerbeau J F, Perthame B. Derivation of viscous Saint-Venant system for laminar shallow water, Numerical validation. Discrete Contin Dyn Syst Ser B, 2001, 1(1): 89–102

[8] Guo Z H, Li H L, Xin Z. Lagrange structure and dynamics for spherically symmetric compressible Navier-Stokes equations. Comm Math Phys, 2012, 309(2): 371–412

[9] Guo Z H, He W. Interface behavior of compressible Navier-Stokes equations with discontinuous boundary conditions and vacuum. Acta Math Sci, 2011, 31B(3): 934–952

[10] Li H L, Li J, Xin Z. Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations. Comm Math Phys, 2008, 281: 401–444

[11] Lian R, Guo Z H, Li H L. Dynamical behavior of vacuum states for 1D compressible Navier-Stokes equations. J Differ Equ, 2010, 248(8): 1926–1954

[12] Marche F. Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects. European J Mech B/Fluids, 2007, 26: 49–63

[13] Nishida T. Equations of fluid dynamics-free surface problems. Comm Pure Appl Math, 1986, 39: 221–238

[14] Okada M, Makino T. Free boundary value problems for the equation of spherically symmetrical motion of viscous gas. Japan J Appl Math, 1993, 10: 219–235

[15] Pedlosky J. Geophysical Fluid Dynamics. New York: Springer-Verlag, 1979

[16] Qin X, Yao Z. Global smooth solutions of the compressible Navier-Stokes equations with density-dependent viscosity. J Differ Equ, 2008, 244(8): 2041–2061

[17] Qin X, Yao Z, Zhao H. One dimensional compressible Navier-Stokes equations with density-dependent viscosity and free boundaries. Comm Pure Appl Anal, 2008, 7(2): 373–381

[18] Secchi P, Valli A. A free boundary problem for compressible viscous fluids. J Reine Angew Math, 1983, 341: 1–31

[19] Serrin J. Mathematical Principles of Classical Fluid Mechanics. Handbuch der Physik, Vol 8/1. Springer-Verlag, 1959: 125–263

[20] Wei M, Zhang T, Fang D. Global behavior of spherically symmetric Navier-Stokes equations with degen-erate viscosity coefficients. SIAM J Math Anal, 2008, 40(3): 869–904

[21] Wang S J, Zhao J N. Global existence of solutions for one-dimensional compressible Navier-Stokes equations in the half space. Acta Math Sci, 2010, 30B(6): 1889–1905

[22] Yang T, Zhao H J. A vacuum problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. J Differ Equ, 2002, 184: 163–184

[23] Yang T, Zhu C J. Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum. Comm Math Phys, 2002, 230: 329–363

[24] Yao L, Wang W J. Compressible Navier-Stokes equations with density-dependent viscosity, vacuum and gravitional force in the case of general pressure. Acta Math Sci, 2008, 28B(4): 801–817