THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS*

doi:10.1007/s10473-023-0617-2

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2597-2614.doi: 10.1007/s10473-023-0617-2

THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS^*

Haoguang LI^1,2,†, Chaojiang XU³

1. School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China;
2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles, MIIT, Nanjing 210016, China;
3. School of Mathematics and Key Laboratory of Mathematical MIIT, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

收稿日期:2022-04-25 修回日期:2023-05-20 发布日期:2023-12-08
通讯作者: †Haoguang LI, E-mail: lihaoguang@scuec.edu.cn
作者简介:Chaojiang XU, E-mail: xuchaojiang@nuaa.edu.cn
基金资助:
Li's research was supported by the Natural Science Foundation of Hubei Province, China (2022CFB444) and the Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA). Xu's research was supported by the NSFC (12031006) and the Fundamental Research Funds for the Central Universities of China.

THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS^*

Haoguang LI^1,2,†, Chaojiang XU³

1. School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China;
2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles, MIIT, Nanjing 210016, China;
3. School of Mathematics and Key Laboratory of Mathematical MIIT, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2022-04-25 Revised:2023-05-20 Published:2023-12-08
Contact: †Haoguang LI, E-mail: lihaoguang@scuec.edu.cn
About author:Chaojiang XU, E-mail: xuchaojiang@nuaa.edu.cn
Supported by:
Li's research was supported by the Natural Science Foundation of Hubei Province, China (2022CFB444) and the Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA). Xu's research was supported by the NSFC (12031006) and the Fundamental Research Funds for the Central Universities of China.

摘要/Abstract

摘要： In this work, we study the linearized Landau equation with soft potentials and show that the smooth solution to the Cauchy problem with initial datum in $L^{2}(\mathbb{R}^3)$ enjoys an analytic regularization effect, and that the evolution of the analytic radius is the same as the heat equations.

关键词: linear Landau equation, analytic smoothing effect, soft potential

Abstract: In this work, we study the linearized Landau equation with soft potentials and show that the smooth solution to the Cauchy problem with initial datum in $L^{2}(\mathbb{R}^3)$ enjoys an analytic regularization effect, and that the evolution of the analytic radius is the same as the heat equations.

Key words: linear Landau equation, analytic smoothing effect, soft potential

中图分类号:

35B65

Haoguang LI, Chaojiang XU. THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS^*[J]. 数学物理学报(英文版), 2023, 43(6): 2597-2614.

Haoguang LI, Chaojiang XU. THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS^*[J]. Acta mathematica scientia,Series B, 2023, 43(6): 2597-2614.

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THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS^*

THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS^*

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