On nonlinear stability of polytropic galaxies
Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 1, p. 15-48
@article{AIHPC_1999__16_1_15_0,
author = {Wolansky, G.},
title = {On nonlinear stability of polytropic galaxies},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Gauthier-Villars},
volume = {16},
number = {1},
year = {1999},
pages = {15-48},
zbl = {0927.70019},
mrnumber = {1668556},
language = {en},
url = {http://www.numdam.org/item/AIHPC_1999__16_1_15_0}
}

Wolansky, G. On nonlinear stability of polytropic galaxies. Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 1, pp. 15-48. http://www.numdam.org/item/AIHPC_1999__16_1_15_0/

[1] A.V. Antonov, Remarks on the problems of stability in stellar dynamics, Soviet Astr, AJ., Vol. 4, 1961, pp. 859-867. | MR 131633

[2] A.V. Antonov, Solution of the problem of stability of a stellar system with the Emden density law and spherical velocity distribution, J. Leningrad Univ. Ser. Mekh. Astro., 1962, Vol. 7, pp. 135-146.

[3] J. Batt, Global symmetric solutions of the initial value problem of stellar dynamics, J. Diff Eq., 1977, Vol. 25, pp. 342-364. | MR 487082 | Zbl 0366.35020

[4] J. Batt, W. Faltenbacher and E. Horst, Stationary spherically symmetric models in stellar dynamics, Arch. for Mech. and Anal., 1986, Vol. 93, pp. 159-183. | MR 823117 | Zbl 0605.70008

[5] J. Batt and K. Pfaffelmoser, On the radius continuity of the models of Polytropic gas spheres which corresponds to the positive solutions of the generalized Emden-Fowler equation, Math. Meth. in the Appl. Sci., 1988, Vol. 10, pp. 499-516. | MR 965418 | Zbl 0676.34017

[6] J. Batt and G. Rein, A rigorous stability result for the Vlasov-Poisson system in three dimensions, Anal. di Mat. Pura ed Applicata, 1993, Vol. CLXIV, pp. 133-154. | MR 1243953 | Zbl 0791.49030

[7] J. Binney and S. Tremaine, Galactic Dynamics, Princeton University Press, Princeton, 1987.

[8] A.M. Fridman and V.L. Polyachenko, Physics of Gravitating Systems, Vol. I&II, Springer Verlag, New York, Berlin, Heidelberg, Tokyo, 1984.

[9] D.D. Holm, J.E. Marsden, T. Ratiu and A. Weinstein, Nonlinear stability of fluid and plasma equilibria, Physics Reports, 1985, Vol. 123, Nos. 1 and 2, pp. 1-116. | MR 794110 | Zbl 0717.76051

[10] C. Marchioro and M. Pulvirenti, A note on the nonlinear stability of a spatially symmetric Vlasov-Poisson flow Math. Meth. in the Appl. Sci., 1986, Vol. 8, pp. 284-288. | MR 845931 | Zbl 0609.35008

[11] G. Rein, Nonlinear stability for the Vlasov Poisson system; the energy-Casimir method, preprint.

[12] J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Commun. Part. Diff. Eqns., 1991, Vol. 16, pp. 1313-1335. | MR 1132787 | Zbl 0746.35050

[13] W.J. Van Den Broek and F. Verhulst, A generalized Lane-Emden-Fowler equation, Math. Meth. in the Appl. Sci., 1982, Vol. 4, pp. 259-271. | MR 659041 | Zbl 0493.35046

[14] Y.H. Wan, Nonlinear stability of stationary spherically symmetric models in stellar dynamics, Arch. Rational. Mech. Anal., 1990, Vol. 112, pp. 83-95. | MR 1073627 | Zbl 0727.70015

[15] J.S. Wong, On the generalized Emden-Fowler equation, S.I.A.M. Review, 1975, Vol. 17, pp. 339-360. | MR 367368 | Zbl 0295.34026