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arXiv · 2205.02992

Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials

Hongmei Cao·Wei-Xi Li·Chao-Jiang Xu
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Abstract

We study the spatially inhomogeneous Landau equations with hard potential in the perturbation setting, and establish the analytic smoothing effect in both spatial and velocity variables for a class of low-regularity weak solutions. This shows the Landau equations behave essentially as the hypoelliptic Fokker-Planck operators. The spatial analyticity relies on a new time-average operator, and the proof is based on a straightforward energy estimate with a careful estimate on the derivatives with respect to the new time-average operator.

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Hongmei Cao, Wei-Xi Li, Chao-Jiang Xu. 2022-05-06. Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials. https://arxiv.org/abs/2205.02992

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