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

被引：4
作者：
Cao, Hongmei [1 ,2 ]
Li, Wei-Xi [3 ,4 ]
Xu, Chao-Jiang [1 ,2 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut, Coll Math, Nanjing 210016, Peoples R China
[2] Nanjing Univ Aeronaut & Astronaut, Key Lab Math MIIT, Nanjing 210016, Peoples R China
[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
[4] Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Hubei, Peoples R China
来源：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2023年 / 176卷
关键词：
Landau equations; Analytic regularization; Subelliptic equations; HOMOGENEOUS BOLTZMANN-EQUATION; CAUCHY-PROBLEM; GEVREY REGULARITY; GLOBAL EXISTENCE; WEAK SOLUTIONS; ANGULAR CUTOFF; HYPOELLIPTICITY; PROPAGATION;
D O I：
10.1016/j.matpur.2023.06.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.(c) 2023 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：138 / 182
页数：45
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