TY - JOUR
T1 - Global-in-Time $L^p−L^q$ Estimates for Solutions of the Kramers-Fokker-Planck Equation
AU - Wang , Xue-Ping
AU - Zhu , Lu
JO - Communications in Mathematical Research 
VL - 4
SP - 560
EP - 578
PY - 2022
DA - 2022/10
SN - 38
DO - http://doi.org/10.4208/cmr.2021-0081
UR - https://global-sci.org/intro/article_detail/cmr/21072.html
KW - Global-in-time estimates, non-self-adjoint operators, kinetic equation, Kramers-Fokker-Planck operator.
AB - <p style="text-align: justify;">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.</p>