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

Carole Rosier (1) , Lionel Rosier (2)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville
2 CORIDA - Robust control of infinite dimensional systems and applications

We 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.

Mots clés: Smoluchowski–Poisson system; Global existence; Uniqueness; Asymptotic behavior

Domaines: Equations aux dérivées partielles [math.AP]

Carole Rosier, Lionel Rosier. On the global existence of solutions for a non-local problem occurring in statistical mechanics. Nonlinear Analysis: Theory, Methods and Applications, 2005, 60 (8), pp.1509-1531. ⟨10.1016/j.na.2004.11.021⟩. ⟨hal-00146466⟩