Blowup of smooth solutions for relativistic Euler equations

Communications in Mathematical Physics

Volumn 262, Issue 3, 2006, Pages 729-755

  Pan, Ronghua ^a   Smoller, Joel A ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31744447499     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1464-9     Document Type: Article

References (16)

1. Dafermos, C.: Hyperbolic conservation laws in continuum physics. Berlin-Heidelberg-New York: Springer-Verlag, 2000
2. Guo, Y., Tahvildar-Zadeh, S.: Formation of singularities in relativistic Fluid dynamics and in spherically symmetric plasma dynamics. Contemp. Math. 238, 151-161 (1999)
3. Kato, T.: The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Ration. Mech. Anal. 58, 181-205 (1975)
4. Lax, P.: Development of singularity of solutions of non linear hyperbolic partial differential equations. J. Math. Phys. 5, 611-613 (1964)
5. Liu, T.: The development of singularity in the nonlinear waves for quasi-linear hyperbolic partial differential equations. J. Differ. Eqs. 33, 92-111 (1979)
6. Makino, T., Ukai, S.: Local smooth solutions of the relativistic Euler equation. J. Math. Kyoto Univ. 35-1, 105-114 (1995)
7. Makino, T., Ukai, S.: Local smooth solutions of the relativistic Euler equation. II. Kodai Math. J. 18, 365-375 (1995)
8. Makino, T., Ukai, S., Kawashima, S.: Sur la solutions á support compact de l'equation d'Euler compressible. Japan J. Appl. Math. 3, 249-257 (1986)
9. Perthame, B.: Non-existence of global solutions to Euler-Poisson equations for repulsive forces. Japan J. Appl. Math. 7, 363-367 (1990)
10. Rendall, A.: The initial value problem for self-gravitating fluid bodies. Mathematical Physics X (Leipzig, 1991), Berlin: Springer, 1992 pp. 470-474
11. Sideris, T.: Formation of singularity in three-dimensional compressible fluids. Commun. Math. Phys. 101, 475-485 (1985)
12. Sideris, T.: Formation of singularities of solutions to nonlinear hyperbolic equations. Arch. Ration. Mech. Anal. 86, 369-381 (1984)
13. Smoller, J.: Shock waves and reaction diffusion equations Berlin-Heidelberg-New York: Springer-Verlag, 2nd Edition, 1993
14. Smoller, J., Temple, B.: Global solutions of the relativistic Euler equations. Commun. Math. Phys 156, 67-99 (1993)
15. Weinberg, S.: Gravitation and Cosmology: principles and applications of the general theory of relativity. New York: Wiley, 1972
16. Xin, Z.: Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density. Comm. Pure Appl. Math. 51, 229-240 (1998)