(untitled) (Communications in Mathematical Research, 2022)
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 one third derivatives of the Kramers-Fokker-Planck operator.