Year: 2022
Author: Xue-Ping Wang, Lu Zhu
Communications in Mathematical Research , Vol. 38 (2022), Iss. 4 : pp. 560–578
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2021-0081
Communications in Mathematical Research , Vol. 38 (2022), Iss. 4 : pp. 560–578
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Global-in-time estimates non-self-adjoint operators kinetic equation Kramers-Fokker-Planck operator.