Remarks on spherically symmetric solutions of the compressible Euler equations

Royal Society of Edinburgh - Proceedings A

Volumn 127, Issue 2, 1997, Pages 243-259

  Chen, Gui Qiang ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744431776     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500023635     Document Type: Article

References (20)

1. G.-Q. Chen. The compensated compactness method and the system of isentropic gas dynamics (MSRI Preprint 00527-91, Berkeley, 1990).
2. G.-Q. Chen and J. Glimm. Global solutions to the compressible Euler equations with geometrical structure. Commun. Math. Phys. 180 (1996) 153-93.
3. P. Constantin and C. Foias. Navier-Stokes Equations (Chicago: University of Chicago Press, 1988).
4. R. Courant and K. O. Friedrichs. Supersonic Flow and Shock Waves (New York: Springer, 1948).
5. C. Dafermos and L. Hsiao. Hyperbolic systems balance laws with inhomogeneity and dissipation. Indiana Univ. Math. J. (c) 31 (1982), 471-91.
6. X. Ding, G.-Q. Chen and P. Luo. Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics. Comm. Math. Phys. 121 (1989), 63-84.
7. R. DiPerna. Convergence of approximate solutions to conservation laws. Arch. Rational Mech. Anal. 82 (1983), 27-70.
8. D. Hoff. Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large, discontinuous initial data. Ind. Univ. Math. J. 41 (1992) 1225-302.
9. P. D. Lax. Shock waves and entropy. In Contributions to Nonlinear Functional Analysis, ed. E. A. Zarantonello, 603-34 (New York: Academic Press, 1971).
10. T.-P. Liu. Quasilinear hyperbolic system. Comm. Math. Phys. 68 (1979), 141-172.
11. A. Majda. Hyperbolic Conservation Laws and Compressible Flows in Several Space Variables (New York: Springer, 1984).
12. T. Makino, K. Mizohata and S. Ukai. Global weak solutions of the compressible Euler equations with spherical symmetry I, II. Japan J. Indust. Appl. Math. 9 (1992), 431-49.
13. T. Makino and S. Takeno. Initial boundary value problem for the spherically symmetric motion of isentropic gas. Japan. J. Indust. Appl. Math. 11 (1994), 171-83.
14. -1,q est compacte pour tout q < 2. J. Math. Pures Appl. 60 (1981), 309-22.
15. M. Okada and T. Makino. Free boundary problem for the equation of spherically symmetric motion of viscous gas. Japan. J. Indust. Appl. Math. 10 (1993), 219-35.
16. S. Rosseland. The Pulsation Theory of Variable Stars (New York: Dover, 1964).
17. M. Slemrod. Resolution of the spherical piston problem for compressible isentropic gas dynamics via a self-similar viscous limit. Proc. Royal Soc. Edinburgh 126 (1996) 1309-40.
18. L. Tartar. Compensated compactness and applications to partial differential equations. Research Notes in Mathematics, Nonlinear Analysis and Mechanics 4, ed. R. J. Knops (New York: Pitman Press, 1979).
19. G. B. Whitham. Linear and Nonlinear Waves (New York: John Wiley, 1974).
20. T. Yang. A functional integral approach to shock wave solutions of the Euler equations with spherical symmetry (Ph.D. Thesis, UC at Davis, 1992).