[1] Bae H O. Existence, regularity and decay rate of solutions of non-Newtonian flow. J Math Anal Appl, 1999, 231: 467–491
[2] Beir˜ao da Veiga H. Long time behavior for one-dimensional motion of a general barotropic viscous fluid. Arch Ration Mech Anal, 1989, 108: 141–160
[3] Bohme G. Non-Newtonian Fluid Mechanics. New York: North-Holland, 1987
[4] Cho Y, Kim H. On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities. Manuscripta Math, 2006, 120: 92–129
[5] Choe H J, Kim H. Global existence of the radially symmetric solutions of the radially symmetric solutions of the Navier-Stokes equation for the isentropic compressible fluids. Math Models Methods Appl Sci, 2005, 28: 1–28
[6] Ding S J, Wen H Y, Zhu C J. Global classical large solutions to 1D compressible Navier-Stokes equations with density-dependent viscosity and vacuum. J Differ Equ, 2011, 251: 1696–1725
[7] Fang L, Guo Z H. A blow-up criterion for a class of non-Newtonian fluids with singularity and vacuum. Acta Math Appl Sin, 2013, (3): 502–515
[8] Fang L, Guo Z H. Analytical solutions to a class of non-Newtonian fluids with free boundaries. J Math Phys, 2012, 53: 103701
[9] Feireisl E, Novotn´y A, Petzeltov´a H. On the existence of globally defined weak solution to the Navier-Stokes equations. J Math Fluid Mech, 2001, (3): 358–392
[10] Galdi G P. An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol I. New York: Springer-Verlag, 1994
[11] Guo B L, Zhu P C. Algebraic L2-decay for the solution to a class system of non-Newtonian fluid in RN. J Math Phys, 2000, 41: 349–356
[12] Huilgol R R. Continuum Mechanics of Viscoelastic Liquids. Delhi: Hindustan Publishing Corporation, 1975
[13] Jiang S, Zhang P. On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations. Comm Math Phys, 2001, 215: 559–581
[14] Kazhikhov A V. Stabilization of solutions of an initial-boundary-value problem for the equations of motion of a barotropic viscous fluid. Differ Equ, 1979, 15: 463–467
[15] Ladyzhenskaya O A. On nonlinear problems of continuum mechanics//Proc Internat Congr Math (Moscow 1966). Moscow: Nauka, 1968: 560–573; English translation in: Amer Math Soc Translation, 1968, 70(2)
[16] Ladyzhenskaya O A. New equations for description of motion of viscous incompressible fluids and global solvability of boundary value problems for their boundary value problems. Proc Steklov Inst Math, 1967,
102: 85–104
[17] Ladyzhenskaya O A. On some modifications of the Navier-Stokes equations for large gradient of velocity. Zap Nauchn Sem Leningrad Odtel. Mat Inst Steklov (LOMI), 1968, 7: 126–154; English translation in: Sem Math V A Steklov Math Inst Leningrad, 1968, (7)
[18] Ladyzhenskaya O A, Seregin G A. On partial regularity of suitable weak solutions to the three-dimensional Navier-Stokes equations. J Math Fluid Mech, 1999, (1): 356–387
[19] Ladyzhenskaya O A. New equations for the description of the viscous incompressible fluids and solvability in the large of the boundary value problems for them//Boundary Value Problems of Mathematical Physics V. Providence RI: Amer Math Soc, 1970[20] Lions P L. Mathematical Topics in Fluid Mechanics, Vol 2: Compressible Fluids. Oxford Lecture Ser Math Appl, Vol 10. Oxford: Clarendon Press, 1998
[21] Liu T P, Xin Z P, Yang T. Vacuum states of compressible flow. Discrete Contin Dyn Syst, 1998, (4): 1–32
[22] M´alek J, Neˇcas J, Rokyta M, et al. Weak and Measure-Valued Solutions to Evolutionary PDEs. New York: Chapman and Hall, 1996
[23] Mamontov A E. Existence of global solutions of multidimensional Burger’s equations of a compressible viscous fluid. Mat Sb, 1999, 19: 61–80
[24] Mamontov A E. Global solvability of the multidiensional Navier-Stokes equations of a compressible fluid with nonlinear viscosity. I. Sib Mat Zh, 1999, 40: 408–420
[25] Mamontov A E. Global solvability of the multidiensional Navier-Stokes equations of a compressible fluid with nonlinear viscosity. II. Sib Mat Zh, 1999, 40: 635–649
[26] Matsumura A, Yanagi S. Uniform boundedness of the solutions for a one dimensional isentropic model system of compressible viscous gas. Comm Math Phys, 1996, 175: 259–274
[27] Neˇcasov´a ˇ S, Luk´aˇcov´a M. Bipolar isothermal non-Newtonian compressible fluids. J Math Anal Appl, 1998, 225: 168–192
[28] Neˇcasov´a ˇ S, Luk´aˇcov´a M. Bipolar barotropic non-Newtonian compressible fluids. Comm Math Univ Carolin, 1994, 35: 467–483
[29] Neˇcas J, Novotn´y A. Some qualitative properties of the viscous compressible heat conductive multipolar fluid. Comm Partrial Differential Equations, 1991, 16: 197–220
[30] Neˇcas J, Novotn´y A, ˇ Silhav´y M. Global solution to the compressible isothermal multipolar fluid. J Math Anal Appl, 1991, 162: 223–241
[31] Schwalter W R. Mechanics of Non-Newtonian Fluid. New York: Pergamon Press, 1978
[32] Solonnikov V A, Kazhikhov A V. Existence theorem for the equations of motion of a compressible viscous fluid. Annu Rev Fluid Mech, 1981, 13: 79–95
[33] Whitaker S. Introduction to Fluid Mechanics. Melbourne, FL: Krieger, 1981
[34] Xin Z P. Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density. Comm Pure Appl Math, 1998, 51: 229–240
[35] Yang T, Yao Z A, Zhu C J. Compressible Navier-Stokes equaitons with density-dependent viscosity and vacuum. Comm Partial Differential Equaitons, 2001, 26: 965–981
[36] Yang T, Zhu C J. Compressible Navier-Stokes equaitons with degenerate viscosity coefficient and vacuum. bComm Partial Differential Equaitons, 2002, 230: 329–363
[37] Yin L, Xu X J, Yuan H J. Global existence and uniqueness of solution of the initial boundary value problem for a class of non-Newtonian fluids with vacuum. Z Angew Math Phys, 2008, 59: 457–474
[38] Yuan H J, Xu X J. Existence and uniqueness of solutions for a class of non-Newtonian fluds with singularity and vacuum. J Differential Equations, 2008, 245: 2871–2916
[39] Yuan H J, Li H P. Existence and uniqueness of solutions for a class of non-Newtonian fluds with vacuum and damping. J Math Anal Appl, 2012, 391: 223–239
[40] Yuan H J, Li H Z, Qiao J Z, Li F P. Global existence of strong solutions of Navier-Stokes equations withnon-Newtonian potential for one-dimensional isentropic compressible fluids. Acta Math Sci, 2012, 32B:1467–1486