On nonlinear stability of polytropic galaxies

G. Wolansky

Annales de l'I.H.P. Analyse non linéaire (1999)

  • Volume: 16, Issue: 1, page 15-48
  • ISSN: 0294-1449

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Wolansky, G.. "On nonlinear stability of polytropic galaxies." Annales de l'I.H.P. Analyse non linéaire 16.1 (1999): 15-48. <http://eudml.org/doc/78458>.

@article{Wolansky1999,
author = {Wolansky, G.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {spherically-symmetric rotating galaxies; uniform estimate on mass distribution; stationary solutions; Vlasov-Poisson system; Newtonian potential; generalized Emden-Fowler law; spherically symmetric perturbations; energy-Casimir method},
language = {eng},
number = {1},
pages = {15-48},
publisher = {Gauthier-Villars},
title = {On nonlinear stability of polytropic galaxies},
url = {http://eudml.org/doc/78458},
volume = {16},
year = {1999},
}

TY - JOUR
AU - Wolansky, G.
TI - On nonlinear stability of polytropic galaxies
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1999
PB - Gauthier-Villars
VL - 16
IS - 1
SP - 15
EP - 48
LA - eng
KW - spherically-symmetric rotating galaxies; uniform estimate on mass distribution; stationary solutions; Vlasov-Poisson system; Newtonian potential; generalized Emden-Fowler law; spherically symmetric perturbations; energy-Casimir method
UR - http://eudml.org/doc/78458
ER -

References

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  1. [1] A.V. Antonov, Remarks on the problems of stability in stellar dynamics, Soviet Astr, AJ., Vol. 4, 1961, pp. 859-867. MR131633
  2. [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. [3] J. Batt, Global symmetric solutions of the initial value problem of stellar dynamics, J. Diff Eq., 1977, Vol. 25, pp. 342-364. Zbl0366.35020MR487082
  4. [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. Zbl0605.70008MR823117
  5. [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. Zbl0676.34017MR965418
  6. [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. Zbl0791.49030MR1243953
  7. [7] J. Binney and S. Tremaine, Galactic Dynamics, Princeton University Press, Princeton, 1987. 
  8. [8] A.M. Fridman and V.L. Polyachenko, Physics of Gravitating Systems, Vol. I&II, Springer Verlag, New York, Berlin, Heidelberg, Tokyo, 1984. Zbl0543.70010
  9. [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. Zbl0717.76051MR794110
  10. [10] C. Marchioro and M. Pulvirenti, A note on the nonlinear stability of a spatially symmetric Vlasov-Poisson flowMath. Meth. in the Appl. Sci., 1986, Vol. 8, pp. 284-288. Zbl0609.35008MR845931
  11. [11] G. Rein, Nonlinear stability for the Vlasov Poisson system; the energy-Casimir method, preprint. 
  12. [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. Zbl0746.35050MR1132787
  13. [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. Zbl0493.35046MR659041
  14. [14] Y.H. Wan, Nonlinear stability of stationary spherically symmetric models in stellar dynamics, Arch. Rational. Mech. Anal., 1990, Vol. 112, pp. 83-95. Zbl0727.70015MR1073627
  15. [15] J.S. Wong, On the generalized Emden-Fowler equation, S.I.A.M. Review, 1975, Vol. 17, pp. 339-360. Zbl0295.34026MR367368

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