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Nonlinear stability of stationary spherically symmetric models in stellar dynamics

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References

  1. Antonov, V. A., Remarks on the problems of stability in stellar dynamics, Soviet Astronomy, AJ. 4 (1961), 859–867.

    Google Scholar 

  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. Mat., Mekh. Astro. 7, 135–46 (1962).

    Google Scholar 

  3. Arnol'd, V. I., Conditions for nonlinear stability of the stationary plane curvilinear flows of an ideal fluid, Soviet Math. Dokl. 6, 773–777 (1965).

    Google Scholar 

  4. Batt, J., Global symmetric solutions of the initial value problem of stellar dynamics, J. Diff. Equations 25, 342–364 (1977).

    Google Scholar 

  5. Batt, J., “The nonlinear Vlasov-Poisson system of partial differential equations in stellar dynamics”, Publications de l'.U.R.E. Math. Pures et Appl. 5, 1–30 (1983).

    Google Scholar 

  6. Batt, J., The present state of the investigation of the Vlasov-Poisson system and of the Vlasov-Maxwell system in stellar dynamics and plasma physics, preprint, Ludwig-Maximilians-Universität München, 1988.

  7. Doremus, J. P., Feix, M. R., & Baumann, G., Stability of Encounterless Spherical Stellar Systems. Phys. Rev. Letters 26, 725–728 (1971).

    Google Scholar 

  8. Fridman, A. M. & Polyachenko, V. L., Physics of Gravitating Systems I, Equilibrium and Stability, Springer-Verlag, 1984.

  9. Gillon, D., Doremus, J. P., & Baumann, G., Stability of self-gravitating systems with phase space density a function of energy and angular momentum for aspherical modes, Astron. & Astrophys. 48, 467–474 (1976).

    Google Scholar 

  10. Holm, D., Marsden, J., Ratiu, J., & Weinstein, A., Nonlinear stability of fluid and plasma equilibria, Physics Reports 123, 1–116 (1985).

    Google Scholar 

  11. Hénon, M., Numerical experiments on the stability of stellar systems, Astron. and Astroph. 24, 229–238 (1973).

    Google Scholar 

  12. Lewis, D., Marsden, J. E., & Ratiu, T., Stability and bifurcation of a rotating planar liquid drop, J. Math. Phys. 28, (1987).

  13. Marsden, J. E., A group theoretic approach to the equations of plasma physics, Can. Math. Bull. 25, 129–142 (1982).

    Google Scholar 

  14. Sygnet, J. F., Forets, G. D., Lachieze-Rey, M., & Pellat, R., Stability of gravitational systems and gravothermal catastrophe in astrophysics, The Astrophysical Journal 276, 737–745 (1984).

    Google Scholar 

  15. Wan, Y. H., The stability of rotating vortex patches, Comm. in Math. Physics 107, 1–20 (1986).

    Google Scholar 

  16. Wan, Y. H., Variational principles for Hill's spherical vortex and nearly spherical vortices, Trans, of Amer. Math. Soc., 1988.

  17. Wan, Y. H., & Pulvirenti, M., Nonlinear stability of circular vortex patches, Comm. in Math. Physics 99, 435–450 (1985).

    Google Scholar 

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Communicated by P. Holmes

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Wan, Y.H. Nonlinear stability of stationary spherically symmetric models in stellar dynamics. Arch. Rational Mech. Anal. 112, 83–95 (1990). https://doi.org/10.1007/BF00431724

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