Relative equilibria in continuous stellar dynamics

Juan Campos Serrano (1) , Manuel del Pino (2) , Jean Dolbeault (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 DIM - Departamento de Ingeniería Matemática [Santiago]

We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose supports are made of an arbitrarily large number of disjoint compact sets, in the low angular velocity and large scale limit. At first order, the solutions behave like point particles, thus making the link with the relative equilibria} in N-body dynamics.

Mots clés: Stellar dynamics; gravitation; mass; rotation; angular velocity; solutions with compact support; radial solutions; symmetry breaking; orbital stability; elliptic equations; variational methods; critical points; finite dimensional reduction; N-body problems; relative equilibria

Domaines: Equations aux dérivées partielles [math.AP]

Juan Campos Serrano, Manuel del Pino, Jean Dolbeault. Relative equilibria in continuous stellar dynamics. Communications in Mathematical Physics, 2010, 300, pp.765-788. ⟨10.1007/s00220-010-1128-2⟩. ⟨hal-00450754⟩