@Article{CMR-38-560,
author = {Wang , Xue-Ping and Zhu , Lu},
title = {Global-in-Time $L^p−L^q$ Estimates for Solutions of the Kramers-Fokker-Planck Equation},
journal = {Communications in Mathematical Research },
year = {2022},
volume = {38},
number = {4},
pages = {560--578},
abstract = {<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>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2021-0081},
url = {http://global-sci.org/intro/article_detail/cmr/21072.html}
}