Existence and stability of Camm type steady states in galactic dynamics

Indiana University Mathematics Journal

Volumn 48, Issue 4, 1999, Pages 1237-1255

  Guo, Yan ^a   Rein, Gerhard ^b  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

Camm distributions; Stability; Stellar dynamics; Vlasov Poisson system

Indexed keywords

EID: 0001307126     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.1999.48.1819     Document Type: Article

References (23)

1. J. J. ALY, On the lowest energy state of a collisionless selfgravitating system under phase space volume constraints, Monthly Notices Royal Astronomical Soc., 241, (1989) 15-27.
2. J. BATT, W. FALTENBACHER & E. HORST, Stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal., 93,(1986) 159-183.
3. J. BATT, P. MORRISON & G. REIN, Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions, Arch. Rational Mech. Anal., 130, (1995) 163-182.
4. P. BRAASCH, G. REIN & J. VUKADINOVIĆ, Nonlinear stability of stationary plasmas - an extension of the energy-Casimir method, Siam J. Applied Math., 59, (1998) 831-844.
5. G. L. CAMM, Self-gravitating systems II, Monthly Notices Royal Astronomical Society, 112, (1952) 155-176.
6. A. M. FRIDMAN & V. L. POLYACHENKO, Physics of Gravitating Systems I, Springer-Verlag, New York 1984.
7. Y. GUO, Stable magnetic equilibria in collisionless plasmas, Comm. Pure and Applied Math., Vol L, (1997) 0891-0933.
8. _ Stable magnetic equilibria in a symmetric collisionless plasma, Commun. Math. Phys., 200, (1999) 211-247.
9. _ Variational method in polytropic galaxies, Arch. Rational Mech. Anal. 150 (1999) 3, 209-224.
10. _ On the generalized Antonov's stability criterion for polytropic steady states, Contem. Math. (2000), in press.
11. Y. GUO & G. REIN, Stable steady states in stellar dynamics, Arch. Rational Mech. Anal. 147 (1999) 225-243.
12. Y. GUO & W. STRAUSS, Nonlinear instability of double-humped equilibria, Ann. Inst. Henri Poincaré, 12, (1995) 339-352.
13. _ Instability of periodic BGK equilibria, Comm. Pure Appl. Math., 48, (1995) 861-894.
14. P.-L. LIONS & B. PERTHAME, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent, math., 105, (1991) 415-430.
15. K. PFAFFELMOSER, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eqns., 95, (1992) 281-303.
16. G. REIN, Nonlinear stability for the Vlasov-Poisson system - the energy-Casimir method, Math. Meth. in the Appl. Sci., 17, (1994) 1129-1140.
17. _ Nonlinear stability of homogeneous models in Newtonian cosmology, Arch. Rational Mech. Anal., 140, (1997) 335-351.
18. _ Flat steady states in stellar dynamics - existence and stability, Commun. Math. Phys. 205 (1999) 1, 229-247.
19. _ Stability of spherically symmetric steady states in galactic dynamics against general perturbations, (1999), Preprint.
20. G. REIN & A. D. RENDALL, Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics, Math. Proc. Camb. Phil. Soc., to appear.
21. J. SCHAEFFER, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Commun. Part. Diff. Eqns., 16, (1991) 1313-1335.
22. Y.-H. WAN, Nonlinear stability of stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal., 112, (1990) 83-95.
23. G. WOLANSKY, On nonlinear stability of polytropic galaxies, Ann. Inst. Henri Poincaré, 16, (1999) 15-48.