Global-in-Time $L^p−L^q$ Estimates for Solutions of the Kramers-Fokker-Planck Equation (Communications in Mathematical Research, 2022)
In this work, we prove an optimal global-in-time $L^p−L^q$ estimate forsolutions to the Kramers-Fokker-Planck equation with short range potential indimension three. Our result shows that the decay rate as $t→ +∞$ is the sameas the heat equation in $x$-variables and the divergence rate as $t→0_+$ is relatedto the sub-ellipticity with loss of one third derivatives of the Kramers-Fokker-Planck operator.
Keywords: Global-in-time estimates; non-self-adjoint operators; kinetic equation; Kramers-Fokker-Planck operator.