---

Journal of Applied Nonlinear Dynamics 5(2) (2016) 231--241 | DOI:10.5890/JAND.2016.06.009

Li Wang; Lei Jin

School of Applied Mathematics, Xiamen, Fujian Province, Xiamen, 361024 China

Download Full Text PDF

 

Abstract

Magnetic fluid is a new type of functional material. The motion of com-pressible, viscous self-gravitating fluids can be expressed by Navier-Stokes-Poisson equations. This study demonstrates the global, non-vacuum solutions with large amplitude to the initialboundary value problem of the one-dimensional compressible Navier- Stokes-Poisson system with degenerate dependent viscosity coefficients and density and temperature dependent heat conductivity coefficients. The main constituent of the detail analysis is to derive the positive lower and upper bounds on the specific volume and the absolute temperature.

Acknowledgments

This research was supported by National Natural Science Foundation of China-NSAF (Nos. 11226174), Xiamen University of Technology Foreign Science and Technology Cooperation and Communication Foundation (E201400200), Xiamen University of Technology High-level personnel Foundation (YKJ14038), Fujian Class A Foundation (JA14242). The writers are very grateful to the editor and the anonymous reviewers for their insightful comments and suggestions.

References

1. [1]	C. Cercignani, R. Illner and M. Pulvirenti, (1994), The Mathematical Theory of Dilute Gases. Applied Mathematical Sciences 106, New York: Springer-Verlag.

2. [2]	S. Chapman and T. G. Colwing, (1990), The Mathematical Theory of Nonuniform Gases. Cambrige Math. Lib., 3rd ed., Cambridge University Press, Cambridge.

3. [3]	C.M. Dafermos and L.Hsiao, (1982), Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity. Nonlinear Anal. 6, 435-454.

4. [4]	H. Grad, (1963), Asymptotic Theory of the Boltzmann Equation II. Rarefied Gas Dynamics. J. A. Laurmann, ed., Vol. 1, New York: Academic Press, 26-59.

5. [5]	J. F. Gerebeau, C. L. Bris, T. Lelievre. (2006), Mathematical methods for the magnetohydrodynamics of liquid metals. Oxford University Press, Oxford.

6. [6]	H. K. Jenssen and T. K. Karper, (2010), One-dimensional compressible flow with temperature dependent transport coefficients. SIAM J. Math. Anal. 42, 904-930.

7. [7]	S. Jiang, (1998), Global smooth solutions of the equations of a viscous, heat-Cconducting, one- dimensional gas with density-dependent viscosity. Math. Nachr. 190(1), 169-183.

8. [8]	S. Kawashima and M. Okada, (1982), Smooth global solutions for the one-dimensional equations in magentohyrodynamics. Proc. Japan Acad.Ser. A Math. Sci. 58, 384-387.

9. [9]	B. Kawohl, (1985), Global existence of large solutions to initial-boundary value problems for a viscous, heatconduting, one-dimensional real gas. J. Differential Equations 58, 76-103.

10. [10]	O. A. Ladyzhenskaya, V. A. (1968), Solonnikov and N. N. Ural’ceva. Linear and quasi-equations of parabolic type. Amer. Math. Sot. Providence, R. I..

11. [11]	T. Lou, (1997), On the outer pressure problem of a viscous heat-conductive one-dimensional real gas. Acta Math. Appl. Sin. Engl. Ser. 13(3) , 251-264.

12. [12]	A. Matsumura and T. Nishida, (1980), The initial value problem for the equations of motion of viscous and heat-conductive gases. J. Math. Kyoto Univ. 20, 67-104.

13. [13]	R. H. Pan, (2011), Privitc communcations.

14. [14]	Z. Tan, T. Yang, H. J. Zhao and Q. Y. Zhou, (2013), Global solutions to the one-dimensional compressible Navier-Stokes-Poisson equations with large data. Society for Industrial and Applied Mathematics. 45 (2), 547-571.

15. [15]	W. G. Vincenti and C. H. Kruger, (1975), Introduction to physical gas dynamics. Cambridge Math.Lib., Krieger, Malabar, FL.

16. [16]	Y. B. Zeldovich and Y. P. Raizer, (1967), Physics of shock waves and High-temperature hydrounamic phenomena. Vol. II, Academic Press, New York.