Year: 2024
Author: Chaojiang Xu, Yan Xu
Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 1 : pp. 88–103
Abstract
In this work, we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework. We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an $L^2$ initial datum for positive time. So that the smoothing effect of the Cauchy problem for the spatially homogeneous Landau equation with hard potentials is exactly same as heat equation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v37.n1.5
Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 1 : pp. 88–103
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Spatially homogeneous Landau equation analytic smoothing effect hard potentials.