Isotropic steady states in galactic dynamics

Communications in Mathematical Physics

Volumn 219, Issue 3, 2001, Pages 607-629

  Guo, Yan ^a   Rein, Gerhard ^b  

^a BROWN UNIVERSITY   (United States)

^b Mathematisches Institut   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035373468     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100434     Document Type: Article

References (22)

1. 1. Aly, J. J.: On the lowest energy state of a collisionless selfgravitating system under phase space volume constraints. Monthly Notices Royal Astronomical Soc. 241, 15-27 (1989)
2. 2. Batt, J., Faltenbacher, W., & Horst, E.: Stationary spherically symmetric models in stellar dynamics. Arch. Rational Mech. Anal. 93, 159-183 (1986)
3. 3. Batt, J., Morrison, P., Rein, G.: Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions. Arch. Rational Mech. Anal. 130, 163-182 (1995)
4. 4. Binney, J., Tremaine, S.: Galactic Dynamics. Princeton: Princeton University Press, 1987
5. 5. Braasch, P., Rein, G., Vukadinović, J.: Nonlinear stability of stationary plasmas - An extension of the energy-Casimir method. SIAM J. Applied Math. 59, 831-844 (1999)
6. 6. Fridman, A. M., Polyachenko, V. L.: Physics of Gravitating Systems, I. New York: Springer-Verlag, 1984
7. 7. Guo, Y.: Variational method in polytropic galaxies. Arch. Rational Mech. Anal. 150, 209-224 (1999)
8. 8. Guo, Y.: On the generalized Antonov's stability criterion. Contem. Math. 263, 85-107 (2000)
9. 9. Guo, Y., Rein, G.: Stable steady states in stellar dynamics. Arch. Rational Mech. Anal. 147, 225-243 (1999)
10. 10. Guo, Y., Rein, G.: Existence and stability of Camm type steady states in galactic dynamics. Indiana University Math. J. 48, 1237-1255 (1999)
11. 11. Guo, Y., Strauss, W.: Nonlinear instability of double-humped equilibria. Ann. Inst. Henri Poincaré 12, 339-352 (1995)
12. 12. Guo, Y., Strauss, W.: Instability of periodic BGK equilibria. Comm. Pure Appl. Math. 48, 861-894 (1995)
13. 13. Lieb, E.H., Loss, M.: Analysis. Providence, RI: American Mathematical Society, 1996
14. 14. Lions, P.-L.: The concentration-compactness principle in the calculus of variations. The locally compact case. Part 1. Ann. Inst. H. Poincaré 1, 109-145 (1984)
15. 15. Pfaffelmoser, K.: Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data. J. Diff. Eqs. 95, 281-303 (1992)
16. 16. Rein, G.: Nonlinear stability for the Vlasov-Poisson system - The energy-Casimir method. Math. Meth. in the Appl. Sci. 17, 1129-1140 (1994)
17. 17. Rein, G.: Flat steady states in stellar dynamics - Existence and stability. Commun. Math. Phys. 205, 229-247 (1999)
18. 18. Rein, G.: Stability of spherically symmetric steady states in galactic dynamics against general perturbations. Preprint, 1999
19. 19. Rein, G., Rendall, A. D.: Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics. Math. Proc. Camb. Phil. Soc. 128, 363-380 (2000)
20. 20. Schaeffer, J.: Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions. Commun. Part. Diff. Eqs. 16, 1313-1335 (1991)
21. 21. Wan, Y.-H.: On nonlinear stability of isotropic models in stellar dynamics. Arch. Rational Mech. Anal. 147, 245-268 (1999)
22. 22. Wolansky, G.: On nonlinear stability of polytropic galaxies. Ann. Inst. Henri Poincaré, 16, 15-48 (1999)