\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

On free boundary problem for compressible navier-stokes equations with temperature-dependent heat conductivity

  • * Corresponding author Zilai Li, Zhenhua Guo

    * Corresponding author Zilai Li, Zhenhua Guo 
Abstract Full Text(HTML) Related Papers Cited by
  • We obtain the existence of global strong solution to the free boundary problem in 1D compressible Navier-Stokes system for the viscous and heat conducting ideal polytropic gas flow, when the heat conductivity depends on temperature in power law of Chapman-Enskog and the viscosity coefficient be a positive constant.

    Mathematics Subject Classification: 35L65;35Q30;76N10.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] S. N. Antontsev, A. V. Kazhikhov and V. N. Monakhov, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, vol. 22 of Studies in Mathematics and its Applications, North-Holland Publishing Co. , Amsterdam, 1990. Translated from the Russian.
    [2] D. Bresch and B. Desjardins, On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids, J. Math. Pures Appl., 87 (2007), 57-90.  doi: 10.1016/j.matpur.2006.11.001.
    [3] S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases, Cambridge University Press, Cambridge, 1990.
    [4] C. M. Dafermos, Global smooth solutions to the initial-boundary value problem for the equations of one-dimensional nonlinear thermoviscoelasticity, SIAM J. Math. Anal., 13 (1982), 397-408.  doi: 10.1137/0513029.
    [5] C. M. Dafermos and L. Hsiao, Global smooth thermomechanical processes in one dimensional nonlinear thermoviscoelasticity, Nonlinear Anal., 6 (1982), 435-454.  doi: 10.1016/0362-546X(82)90058-X.
    [6] E. Feireisl, Dynamics of Viscous Compressible Fluids, Oxford Univ. Press, Oxford, 2004.
    [7] A. Friedman, Partial Differential Equations, Krieger, New York, 1976.
    [8] S. Jiang, On the asymptotic behavior of the motion of a viscous, heat-conducting, one-dimensional real gas, Math. Z., 216 (1994), 317-336.  doi: 10.1007/BF02572324.
    [9] S. Jiang, Large-time behavior of solutions to the equations of a viscous polytropic ideal gas, Annali di Matematica pura ed applicata, 175 (1998), 253-275.  doi: 10.1007/BF01783686.
    [10] S. Jiang, Large-time behavior of solutions to the equations of a one-dimensional viscous polytropic ideal gas in unbounded domains, Comm. Math. Phys., 200 (1999), 181-193.  doi: 10.1007/s002200050526.
    [11] H. K. Jenssen and T. K. Karper, One-dimensional compressible flow with temperature dependent transport coeffcients, SIAM J. Math. Anal., 42 (2010), 904-930.  doi: 10.1137/090763135.
    [12] B. Kawohl, Global existence of large solutions to initial boundary value problems for a viscous, heat-conducting, one-dimensional real gas, J. Differential Equations, 58 (1985), 76-103.  doi: 10.1016/0022-0396(85)90023-3.
    [13] J. I. Kanel, A model system of equations for the one-dimensional motion of a gas, Differencial'nye Uravnenija, 4 (1968), 721-734. 
    [14] A. V. Kazhikhov, On the Cauchy problem for the equations of a viscous gas, (Russian), Sibirsk. Mat. Zh., 23 (1982), 60-64. 
    [15] A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect to time of initialboundary value problems for one-dimensional equations of a viscous gas, J. Appl. Math. Mech., 41 (1977), 273-282.  doi: 10.1016/0021-8928(77)90011-9.
    [16] O. A. Ladyzenskaya, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Sot. , Providence, R. I. , 1968.
    [17] A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104.  doi: 10.1215/kjm/1250522322.
    [18] A. Matsumura and T. Nishida, The initial boundary value problems for the equations of motion of compressible and heat-conductive fluids, Comm. Math. Phys., 89 (1983), 445-464. 
    [19] J. Nash, Le probleme de Cauchy pour les équations différentielles dún fluide général, Bull, Soc. Math. France, 90 (1962), 487-491. 
    [20] T. Nagasawa, On the one-dimensional motion of the polytropic ideal gas nonfixed on the boundary, J. Differential Equations, 65 (1986), 49-67.  doi: 10.1016/0022-0396(86)90041-0.
    [21] R. H. Pan, Global smooth solutions and the asymptotic behavior of the motion of a viscous, heat-conductive, one-dimensional real gas, J. Partial Differential Equations, 11 (1998), 273-288. 
    [22] R. H. Pan and W. Z. Zhang, Compressible Navier-Stokes equations with temperature dependent heat conductivity, Commun. Math. Sci., 13 (2015), 401-425.  doi: 10.4310/CMS.2015.v13.n2.a7.
    [23] A. Tani, On the first initial-boundary value problem of compressible viscous fluid motion, Publ. Res. Inst. Math. Sci. Kyoto Univ., 13 (1977), 193-253.  doi: 10.2977/prims/1195190106.
    [24] H. X. LiuT. YangH. J. Zhao and Q. Y. Zou, One-dimensional compressible Navier-Stokes equations with temperature dependent transport coefficients and large data, SIAM J. Math. Anal., 46 (2014), 2185-2228.  doi: 10.1137/130920617.
    [25] W. G. Vincenti and C. H. Kruger, Jr. , Introduction to Physical Gas Dynamics, Physics Today, 19 (1966), p95. doi: 10.1063/1.3047788.
    [26] H. Y. Wen and C. J. Zhu, Global classical large solutions to Navier-Stokes equations for viscous compressible and heat-conducting fluids with vacuum, SIAM J. Math. Anal., 45 (2013), 431-468.  doi: 10.1137/120877829.
    [27] T. Wang and H. J. Zhao, Global large solutions to a viscous heat-conducting onedimensional gas with temperature-dependent viscosity, Math. Nachr., 190 (1998), 169-183, at arXiv: 1505.05252. doi: 10.1002/mana.19981900109.
    [28] Z. P. Xin, Blow-up of smooth solution to the compressible Navier-Stokes equations with compact density, Commun, Pure Appl. Math., 51 (1998), 229-240.  doi: 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C.
  • 加载中
SHARE

Article Metrics

HTML views(148) PDF downloads(152) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return