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A constraint variational problem arising in stellar dynamics

Author(s): Mahir Hadzic
Journal: Quart. Appl. Math. 65 (2007), 145-153.
MSC (2000): Primary 49K20
Posted: December 14, 2006
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Abstract: We use the compactness result of A. Burchard and Y. Guo to analyze the reduced `energy' functional arising naturally in the stability analysis of steady states of the Vlasov-Poisson system (cf. Sánchez and Soler, to appear, and Hadzic, 2005). We consider the associated variational problem and present a new proof that puts it in the general framework for tackling the variational problems of this type, given by Y. Guo and G. Rein (cf. Rein, 2005 and Rein, 2002).

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Burchard, A., Y. Guo: Compactness via Symmetrization. J. Functional Analysis, 214, 40-73, 2004. MR 2079885 (2005g:46061)

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Hadzic, M.: Compactness and stability of some systems of nonlinear PDE-s in galactic dynamics. Diploma thesis, University of Vienna, 2005.

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Hardy, G., J. E. Littlewood, G. Polya: Inequalities. Cambridge Mathematical Press, Cambridge 1952, 2nd edition. MR 0046395 (13:727e)

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Lieb, E. H., M. Loss: Analysis. American Math. Soc., Providence, 2001. MR 1817225 (2001i:00001)

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Rein, G.: Nonlinear Stability of Newtonian Galaxies and Stars from a Mathematical Perspective, Nonlinear Dynamics in Astronomy and Physics. Annals of the New York Academy of Sciences, 1045, 103-119, 2005.

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Rein, G.: Reduction and a concentration-compactness principle for energy-Casimir functionals. SIAM J. on Math. Anal., 33, 896-912, 2002. MR 1884728 (2003a:35006)

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Sánchez, Ó., J. Soler: Orbital stability for polytropic galaxies. Annales de l'Institut Henri Poincare, ``Analyse non lineaire ". To appear.

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Additional Information:

Mahir Hadzic
Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
Email: hadzic@dam.brown.edu

PII: S0033-569X-06-01032-9
Received by editor(s): April, 2006
Posted: December 14, 2006
Additional Notes: This paper is a part of the author's Diploma thesis. I would like to thank Gerhard Rein for introducing me to the problem and for many stimulating discussions.
Copyright of article: Copyright 2006, Brown University
The copyright for this article reverts to public domain after 28 years from publication.


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