Short and long time behavior of the Fokker-Planck equation in a confining potential and applications

Frédéric Hérau (1)

1 LMR - Laboratoire de Mathématiques de Reims

We consider the linear Fokker-Planck equation in a confining potential in space dimension $d \geq 3$. Using spectral methods, we prove bounds on the derivatives of the solution for short and long time, and give some applications.

Mots clés: Vlasov-Poisson; Poisson-Emden; non-linear PDE; Fokker-Planck; exponential decay; hypoellipticity; entropy; semi-group

Domaines: Equations aux dérivées partielles [math.AP]

Frédéric Hérau. Short and long time behavior of the Fokker-Planck equation in a confining potential and applications. 2008. ⟨hal-00004028v3⟩