GLOBAL-IN-TIME L p − L q ESTIMATES FOR SOLUTIONS OF THE KRAMERS-FOKKER-PLANCK EQUATION

Xue Ping Wang (1) , Lu Zhu

1 LMJL - Laboratoire de Mathématiques Jean Leray

In this work, we prove an optimal global-in-time L p −L q estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three. Our result shows that the decay rate as t → +∞ is the same as the heat equation in x-variables and the divergence rate as t → 0 + is related to the sub-ellipticity with loss of 1/3 derivatives of the Kramers-Fokker-Planck operator.

Domaines: Equations aux dérivées partielles [math.AP]

Xue Ping Wang, Lu Zhu. GLOBAL-IN-TIME L p − L q ESTIMATES FOR SOLUTIONS OF THE KRAMERS-FOKKER-PLANCK EQUATION. 2021. ⟨hal-03280770⟩