关于具有软势能的线性朗道方程时间解析性的备注

IF 0.4 Q4 MATHEMATICS Analysis in Theory and Applications Pub Date : 2024-04-01 DOI:10.4208/ata.oa-2022-0029

Chaojiang Xu, Yan Xu

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引用次数: 0

摘要

在本论文中，我们研究了具有软势能的线性空间均质朗道方程的考奇问题。我们证明，对于正时间，具有 $L^2$ 初始值的时间变量的 Cauchy 问题解具有解析正则化效应。因此，对于具有软势垒的线性空间均相朗道方程，Cauchy 问题的平滑效应与 Heatequation 相似。

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A Remark about Time-Analyticity of the Linear Landau Equation with Soft Potential

In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. 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 Cauchy problem for the linear spatially homogeneous Landau equation with soft potentials is similar to the heat equation.

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Analysis in Theory and Applications

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747