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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).
References:
-
- 1.
- Burchard, A., Y. Guo: Compactness via Symmetrization. J. Functional Analysis, 214, 40-73, 2004. MR 2079885 (2005g:46061)
- 2.
- Hadzic, M.: Compactness and stability of some systems of nonlinear PDE-s in galactic dynamics. Diploma thesis, University of Vienna, 2005.
- 3.
- Hardy, G., J. E. Littlewood, G. Polya: Inequalities. Cambridge Mathematical Press, Cambridge 1952, 2nd edition. MR 0046395 (13:727e)
- 4.
- Lieb, E. H., M. Loss: Analysis. American Math. Soc., Providence, 2001. MR 1817225 (2001i:00001)
- 5.
- 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.
- 6.
- 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)
- 7.
- 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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