Orbital stability for polytropic galaxies
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 6, pp. 781-802. 
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     author = {S\'anchez, \'Oscar and Soler, Juan},
     title = {Orbital stability for polytropic galaxies},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.02.001/}
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Sánchez, Óscar; Soler, Juan. Orbital stability for polytropic galaxies. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 6, pp. 781-802. doi : 10.1016/j.anihpc.2006.02.001. http://www.numdam.org/articles/10.1016/j.anihpc.2006.02.001/

[1] Antonov V.A., Remarks on the problems of stability in stellar dynamics, Soviet Astron. AJ. 4 (1961) 859-867. | MR

[2] Antonov V.A., 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. 7 (1962) 135-146.

[3] Barnes J., Goodman J., Hut P., Dynamical instabilities in spherical stellar systems, Astrophys. J. 300 (1986) 112-131. | MR

[4] J. Batt, A survey of recent results in the investigation of the Vlasov-Poisson system and questions open for further research, in: L.L. Bonilla, B. Perthame, J. Soler, J.L. Vázquez (Eds.), European Workshop on Kinetic Equations, Book of Abstracts, Granada, Spain, 1996.

[5] Batt J., Faltenbacher W., Horst E., Stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal. 93 (2) (1986) 159-183. | MR | Zbl

[6] Cazenave T., An Introduction to Nonlinear Schrödinger Equations, Textos de Métodos Matemáticos, vol. 26, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, 1996.

[7] Cazenave T., Lions P.L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Commun. Math. Phys. 85 (1982) 549-561. | MR | Zbl

[8] Dolbeault J., Sánchez O., Soler J., Asymptotic behaviour for the Vlasov-Poisson system in the stellar dynamics case, Arch. Rational Mech. Anal. 171 (2004) 301-327. | MR | Zbl

[9] Grillakis M., Shatah J., Strauss W., Stability theory of solitary waves in the presence of symmetry, I, J. Func. Anal. 74 (1987) 160-197. | MR | Zbl

[10] Grillakis M., Shatah J., Strauss W., Stability theory of solitary waves in the presence of symmetry, II, J. Func. Anal. 94 (1990) 308-348. | MR | Zbl

[11] Guo Y., Variational method for stable polytropic galaxies, Arch. Rational Mech. Anal. 150 (1999) 209-224. | MR | Zbl

[12] Guo Y., On the generalized Antonov's stability criterion, Contemp. Math. 150 (2000) 85-107. | MR | Zbl

[13] Guo Y., Rein G., Stable steady states in stellar dynamics, Arch. Rational Mech. Anal. 147 (1999) 225-243. | MR | Zbl

[14] Guo Y., Rein G., Isotropic steady states in galactic dynamics, Commun. Math. Phys. 209 (2001) 607-629. | MR | Zbl

[15] Hardy G., Littlewood J.E., Pólya G., Inequalities, Cambridge Mathematical Press, Cambridge, 1952. | MR | Zbl

[16] Hénon M., Numerical experiments on the stability of spherical stellar systems, Astronom. Astrophys. 24 (1973) 229-238.

[17] Lieb E., Loss M., Analysis, American Mathematical Society, Providence, RI, 2001. | MR | Zbl

[18] Lions P.L., Perthame B., Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math. 105 (2) (1991) 415-430. | MR | Zbl

[19] Rein G., Reduction and a concentration-compactness principle for energy-Casimir functionals, SIAM J. Math. Anal. 33 (2001) 896-912. | MR | Zbl

[20] Rein G., Stability of spherically symmetric steady states in galactic dynamics against general perturbations, Arch. Rational Mech. Anal. 161 (2002) 27-42. | MR | Zbl

[21] Schaeffer J., Steady states in galactic dynamics, Arch. Rational Mech. Anal. 172 (2004) 1-19. | MR | Zbl

[22] Wan Y.H., On nonlinear stability of isotropic models in stellar dynamics, Arch. Rational Mech. Anal. 147 (1999) 245-268. | MR | Zbl

[23] Wolansky G., On nonlinear stability of polytropic galaxies, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999) 15-48. | Numdam | MR | Zbl

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