Initial-boundary Value Problems to the One-dimensional Compressible Navier-Stokes-Poisson Equations with viscosity and heat conductivity coefficients

Volume 1, Issue 1, October 2016     |     PP. 71-94      |     PDF (676 K)    |     Pub. Date: October 20, 2016
DOI:    465 Downloads     8434 Views  

Author(s)

Li WANG, School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China
Lei JIN, School of Environment Science and Engineer, Xiamen University of Technology, Xiamen 361024, China

Abstract
Abstract In this paper, the global, non-vacuum solutions with large amplitude to the initial-boundary value problem of the one-dimensional compressible Navier-Stokes-Poisson system with viscosity and heat conductivity coefficients are considered. The proof is based on the analysis on the positive lower and upper bounds on the specific volume and the absolute temperature.

Keywords
compressible Navier-Stokes-Poisson system; global, non-vacuum solutions with large amplitude; viscosity and heat conductivity coefficients

Cite this paper
Li WANG, Lei JIN, Initial-boundary Value Problems to the One-dimensional Compressible Navier-Stokes-Poisson Equations with viscosity and heat conductivity coefficients , SCIREA Journal of Mathematics. Volume 1, Issue 1, October 2016 | PP. 71-94.

References

[ 1 ] Gerebeau, J. F. and Bris, C. L. and Lelievre,T. Mathematical methods for the magneto-hydrodynamics of liquid metals. Oxford University Press, Oxford, (2006)
[ 2 ] Tan, Z., Yang, T., Zhao H. J. and Zhou, Q. Y. Global solutions to the one-dimensional compressible Navier-Stokes-Poisson equations with large data. Society for Industrial and Applied Mathematics, 45(2), 547-571(2013)
[ 3 ] Okada M. and Kawashima, S. On the equations of one-dimensional motion of compressible viscous fluids. J. Math. Kyoto Univ., 1, 55–7123 (1983)
[ 4 ] Grad, H. Asymptotic Theory of the Boltzmann Equation II. Rarefied Gas Dynamics. J. A. Laurmann, ed., Vol. 1, Academic Press, New York, 26-59 (1963)
[ 5 ] Zeldovich, Y. B. and Raizer, Y. P. Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Academic Press, New York, (1967)
[ 6 ] Dafermos, C. M. and Hsiao, C. M. Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity. Nonlinear Anal., 6, 435-454(1982)
[ 7 ] Jenssen, H. K. and Karper, T. K. One-dimensional compressible flow with temperature dependent transport coefficients. SIAM J. Math. Anal., 42, 904-930(2010)
[ 8 ] Jiang, S. and Racke, R. Evolution Equations in Thermoelasticity. Monographs and surveys in pure and applied mathematics, volume 112, Chapman & Hall/CRC Press, Boca Raton, (2000)
[ 9 ] Kawohl, B. Global existence of large solutions to initial-boundary value problems for a viscous, heat-conducting, one-dimensional real gas. J. Differential Equations, 58, 76-103(1985)
[ 10 ] Kawashima, S. and Nishida, T. Global solutions to the initial value problem for the equations of one-dimensional motion of viscous polytrophic gases. J. Math. Kyoto Univ., 21(4), 825-837(1981)
[ 11 ] Kazhikhow, A. V. and Shelukhin, V. V. Unique global solution with respect to time of initial-boundary calue problem for one-dimensional equations of a viscous gas. J. Appl. Math. Mech., 41(2), 273-282(1977)
[ 12 ] Kanel, Y. On a model system of equations of one-dimensional gas motion. Differencial’nya Uravnenija, 4, 374-380(1968)
[ 13 ] Chapman, S. and Colwing, T. G. The Mathematical Theory of Nonuniform Gases. Cambrige Math. Lib., 3rd ed., Cambridge University Press, Cambridge, (1990)
[ 14 ] Vincenti, W. G. and Kruger, C. H. Introduction to physical Gas Dynamics. Cambridge Math. Lib., Cambridge University Press, Cambridge, (1975)
[ 15 ] Tani, A. On the free boundary value problem for compressible viscous fluid motion. J. Math. Kyoto Univ., 21(4), 839–859) (1981)
[ 16 ] Ladyzhenskaya, O. A., Solonnikov, V. A. and Ural’ceva, N. N. Linear and quasi-equations of parabolic type. Amer. Math. Sot., Providence, R. I., (1968)