Kramers-Fokker-Planck方程解的全局时间$L^p−L^q$估计

Pub Date : 2021-07-07 DOI:10.4208/cmr.2021-0081

Xue Ping Wang, Lu Zhu

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引用次数: 2

摘要

在这项工作中，我们证明了三维具有短程势的Kramers-Fokker-Planck方程解的最优全局时间Lp−Lq估计。我们的结果表明→ +∞ 与x变量中的热方程相同，发散率为t→ 0+与Kramers-Fokker-Planck算子的1/3导数损失的亚椭圆率有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Global-in-Time $L^p−L^q$ Estimates for Solutions of the Kramers-Fokker-Planck Equation

In this work, we prove an optimal global-in-time Lp−Lq 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 1/3 derivatives of the Kramers-Fokker-Planck operator.

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