[1] Duan R, Liu H X, Zhao H J. Nonlinear stability of rarefaction waves for the compressible Navier-Stokes equations with large initial perturbation. Trans Amer Math Soc, 2009, 361(1):453-493
[2] Chapman S, Cowling T. The Mathematical Theory of Non-uniform Gases. 3rd ed. London:Cambrige University Press, 1970
[3] Fan L L, Liu H X, Wang T, et al. Inflow problem for the one-dimensional compressible Navier-Stokes equations under large initial perturbation. J Differential Equations, 2014, 257(10):3521-3553
[4] Goodman J. Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch Rational Mech Anal, 1986, 95:325-344
[5] Hong H. Global stability of viscous contact wave for 1-D compressible Navier-Stokes equations. J Differential Equations, 2012, 252(5):3482-3505
[6] Hong H H, Wang T. Stability of stationary to the in flow problem for full compressible Navier-Stokes equations with a large initial perturbation. SIAM J Math Anal, 2017, 49(3):2138-2166
[7] Hong H H, Wang T. Large-time behavior of solutions to the in flow problem offull compressible NavierStokes equations with large perturbation. Nonlinearity, 2017, 30:3010-3039
[8] Huang B K, Wang L S, Xiao Q H. Global nonlinear stability of rarefaction waves for compressible NavierStokes equations with temperature and density dependent transport coefficients. Kinet Relat Models, 2016, 9(3):469-514
[9] Huang B K, Liao Y K. Global stability of combination of viscous contact wave with rarefaction wave for compressible Navier-Stokes equations with temperature-dependent viscosity. Preprint, 2016
[10] Hong H, Huang F M. Asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave for compressible Navier-Stokes equations with free boundary. Acta Mathematica Scientia, 2012, 32B(1):389-412
[11] Huang F M, Li J, Matsumura A. Asymptotic stability of combination of viscous contact wave with rarefaction waves for one-dimensional compressible Navier-Stokes system. Arch Ration Mech Anal, 2010, 197(1):89-116
[12] Huang F M, Li J, Shi X D. Asymptotic behavior of solutions to the full compressible Navier-Stokes equations in the half space. Commun Math Sci, 2010, 8(3):639-654
[13] Huang F M, Matsumura A. Stability of a composite wave of two viscous shock waves for the full compressible Navier-Stokes equation. Comm Math Phys, 2009, 289(3):841-861
[14] Huang F M, Matsumura A, Xin Z P. Stability of contact discontinuities for the 1-D compressible NavierStokes equations. Arch Ration Mech Anal, 2006, 179(1):55-77
[15] Huang F M, Shi X D, Wang Y. Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary. Kinet Relat Models, 2010, 3(3):409-425
[16] Huang F M, Wang T. Stability of superposition of viscous contact wave and rarefaction waves for compressible Navier-Stokes system. Indiana Univ Math J, 2016, 65:1833-1875
[17] Huang F M, Xin Z P, Yang T. Contact discontinuity with general perturbations for gas motions. Adv Math, 2008, 219(4):1246-1297
[18] Huang F M, Zhao H J. On the global stability of contact discontinuity for compressible Navier-Stokes equations. Rend Sem Mat Univ Padova, 2003, 109:283-305
[19] Jiang S. Large-time behavior of solutions to the equations of a one-dimensional viscous polytropic ideal gas in unbounded domains. Comm Math Phys, 1999, 200:181-193
[20] Jiang S. Remarks on the asymptotic behaviour of solutions to the compressible Navier-Stokes equations in the half-line. Proc Roy Soc Edinburgh Sect A, 2002, 132:627-638
[21] Jiang S, Zhang P. Global weak solutions to the Navier-Stokes equations for a 1D viscous polytropic ideal gas. Quart Appl Math, 2003, 61:435-449
[22] Kanel' Ya. A model system of equations for the one-dimensional motion of a gas (Russian). Differencial'nye Uravnenija, 1968, 4:721-734
[23] Kawashima S, Matsumura A. Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion. Comm Math Phys, 1985, 101(1):97-127
[24] Kawashima S, Matsumura A, Nishihara K. Asymptotic behaviour of solutions for the equations of a viscous heat-conductive gas. Proc Japan Acad, 1986, 62A:249-252
[25] Kazhikhove A V. Cauchy problem for viscous gas equations. Siberian Math J, 1982, 23:44-49
[26] Kazhikhov A V, Shelukhin V V. Unique golbal solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas. J Appl Math Mech, 1977, 41(2):273-282; translated from Prikl Mat Meh, 1977, 41(2):282-291(Russian)
[27] Li J, Liang Z L. Some uniform estimates and large-iime behavior of solutions to one-dimensional compressible Navier-Stokes system in unbounded domains with large data. Arch Ration Mech Anal, 2016, 220(3):1195-1208
[28] Liu T P. Shock waves for compressible Navier-Stokes equations are stable. Comm Pure Appl Math, 1986, 39(5):565-594
[29] Liu T P, Xin Z P. Nonlinear stability of rarefaction waves for compressible Navier-Stokes equations. Comm Math Phys, 1988, 118:451-465
[30] Liu T P, Xin Z P. Pointwise decay to contact discontinuities for systems of viscous conservation laws. Asian J Math, 1997, 1:34-84
[31] Liu H X, Yang T, Zhao H J, et al. One-dimensional compressible Navier-Stokes equations with temperature dependent transport coefficients and large data. SIAM Journal on Mathematical Analysis, 2014, 46(3):2185-2228
[32] Matsumura A, Mei M. Convergence to travelling fronts of solutions of the p-system with viscosity in the presence of a boundary. Arch Ration Mech Anal, 1999, 146(1):1-22
[33] Matsumura A, Nishihara K. On the stability of traveling wave solutions of a one-dimensional model system for compressible viscous gas. Japan J Appl Math, 1985, 2:17-25
[34] Matsumura A, Nishihara K. Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas. Japan J Appl Math, 1986, 3(1):1-13
[35] Matsumura A, Nishihara K. Global asymptotics toward the rarefaction wave for solutions of viscous psystem with boundary effect. Quart Appl Math, 2000, 58(1):69-83
[36] Matsumura A, Nishihara K. Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas. Comm Math Phys, 1992, 144(2):325-335
[37] Nishihara K, Yang T, Zhao H J. Nonlinear stability of strong rarefaction waves for compressible NavierStokes equations. SIAM J Math Anal, 2004, 35(6):1561-1597
[38] Smoller J. Shock Waves and Reaction-Diffusion Equations. 2nd edition. Grundlehren der Mathematischen Wissenschaften[Fundamental Principles of Mathematical Sciences]. New York:Springer-Verlag, 1994
[39] Tan A, Yang T, Zhao H J, et al. Global solutions to the one-dimensional compressible Navier-Stokes-Poisson equations with large data. SIAM Journal on Mathematical Analysis, 2013, 45(2):547-571
[40] Wan L, Wang T, Zou Q Y. Stability of stationary solutions to the outflow problem for full compressible Navier-Stokes equations with large initial perturbation. Nonlinearity, 2016, 29(4):1329-1354
[41] Wang T, Zhao H J, Zou Q Y. One-dimensional compressible Navier-Stokes equations with large density oscillation. Kinetic and Related Models, 2013, 6(3):649-670
[42] Zumbrun K. Stability of large-amplitude shock waves of compressible Navier-Stokes equations. With an appendix by Helge Kristian Jenssen and Gregory Lyng. Handbook of Mathematical Fluid Dynamics. Vol. Ⅲ. Amsterdam:North-Holland, 2004
[43] He L, Tand S J, Wang T. Stability viscous shock waves for the one dimensional compressitle Novier-Stokes equations with density-dependent viscosity. Acta Mathematica Scientia, 2016, 36B(1):34-48
