Thermodynamics of self-gravitating systems

Self-gravitating systems are expected to reach a statistical equilibrium state either through collisional relaxation or violent collisionless relaxation. However, a maximum entropy state does not always exist and the system may undergo a ``gravothermal catastrophe'': it can achieve ever increasing values of entropy by developing a dense and hot ``core'' surrounded by a low density ``halo''. In this paper, we study the phase transition between ``equilibrium'' states and ``collapsed'' states with the aid of a simple relaxation equation [Chavanis, Sommeria and Robert, Astrophys. J. 471, 385 (1996)] constructed so as to increase entropy with an optimal rate while conserving mass and energy. With this numerical algorithm, we can cover the whole bifurcation diagram in parameter space and check, by an independent method, the stability limits of Katz [Mon. Not. R. astr. Soc. 183, 765 (1978)] and Padmanabhan [Astrophys. J. Supp. 71, 651 (1989)]. When no equilibrium state exists, our relaxation equation develops a self-similar collapse leading to a finite time singularity.Comment: 54 pages. 25 figures. Submitted to Phys. Rev.

On the global existence of solutions for a non-local problem occurring in statistical mechanics

International audienceWe consider the evolution of the density and temperature of a cloud of self-gravitating particles confined to a ball in \mathbbR{3}. We prove the global in time existence, the uniqueness, and the convergence of the solution toward an equilibrium state when the initial density profile behaves like $1/r^2$ at the origin

Smooth solutions for the motion of a ball in an incompressible perfect fluid

International audienceIn this paper we investigate the motion of a rigid ball surrounded by an incompressible perfect fluid occupying RN. We prove the existence, uniqueness, and persistence of the regularity for the solutions of this fluid-structure interaction problem

Global solutions for a problem modeling the dynamics of a system of self-gravitating Brownian particles

Abstract. Results on the global existence and uniqueness of variational solutions to an elliptic-parabolic problem occurring in statistical mechanics are provided. 1. Introduction. Let B denote the open ball in R3 centered at the origin and with radius 1. We consider the parabolic-elliptic system n = r (()rn+ nr) in B R+; (1.1) = 4n in B R+; (1.2

Etude numerique des equations de Navier-Stokes bidimensionnelles avec conditions aux limites periodiques

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Well posedness of general cross-diffusion systems

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