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Localized minimizers of flat rotating gravitational systems

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Date
2008
Link to item file
http://hal.archives-ouvertes.fr/hal-00112165/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
angular velocity; entropy; diffusion limit; drift-diffusion; Hardy-Littlewood-Sobolev inequality; bounded solutions; critical bifurcation parameter; rotation; mass; symmetry breaking; localized minimizers; radial solutions; minimization; solutions with compact support; Stellar dynamics; gravitation
Journal issue
Annales de l'Institut Henri Poincaré. Analyse non linéaire
Volume
25
Number
6
Publication date
2008
Article pages
1043-1071
Publisher
Elsevier Masson SAS.
DOI
http://dx.doi.org/10.1016/j.anihpc.2007.01.001
URI
https://basepub.dauphine.fr/handle/123456789/770
Collections
  • CEREMADE : Publications
Metadata
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Author
Fernandez, Javier
Dolbeault, Jean
Type
Article accepté pour publication ou publié
Abstract (EN)
We study a two dimensional system in solid rotation at constant angular velocity driven by a self-consistent three dimensional gravitational field. We prove the existence of non symmetric stationary solutions of such a flat system in the rotating frame as long as the angular velocity does not exceed some critical value which depends on the mass. The solutions can be seen as stationary solutions of a kinetic equation with a relaxation-time collision kernel forcing the convergence to the polytropic gas solutions, or as stationary solutions of an extremely simplified drift-diffusion model, which is derived from the kinetic equation by formally taking a diffusion limit. In both cases, the solutions are critical points of a free energy functional, and can be seen as localized minimizers in an appropriate sense. Symmetry breaking occurs for small angular velocities.

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