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
相关论文
共 57 条
  • [11] NONANALYTIC-HYPOELLIPTICITY FOR SOME DEGENERATE ELLIPTIC OPERATORS
    BAOUENDI, MS
    GOULAOUI.C
    [J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 78 (03) : 483 - &
  • [12] Gevrey Smoothing for Weak Solutions of the Fully Nonlinear Homogeneous Boltzmann and Kac Equations Without Cutoff for Maxwellian Molecules
    Barbaroux, Jean-Marie
    Hundertmark, Dirk
    Ried, Tobias
    Vugalter, Semjon
    [J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 225 (02) : 601 - 661
  • [13] Hypoelliptic regularity in kinetic equations
    Bouchut, F
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2002, 81 (11): : 1135 - 1159
  • [14] Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials
    Cameron, Stephen
    Silvestre, Luis
    Snelson, Stanley
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2018, 35 (03): : 625 - 642
  • [15] WELL-POSEDNESS OF CAUCHY PROBLEM FOR LANDAU EQUATION IN CRITICAL BESOV SPACE
    Cao, Hongmei
    Li, Hao-Guang
    Xu, Chao-Jiang
    Xu, Jiang
    [J]. KINETIC AND RELATED MODELS, 2019, 12 (04) : 829 - 884
  • [16] CARRAPATOSO K., 2017, ANN PDE, V3
  • [17] Cauchy Problem and Exponential Stability for the Inhomogeneous Landau Equation
    Carrapatoso, Kleber
    Tristani, Isabelle
    Wu, Kung-Chien
    [J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2016, 221 (01) : 363 - 418
  • [18] The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off
    Chen, Hua
    Hu, Xin
    Li, Wei-Xi
    Zhan, Jinpeng
    [J]. SCIENCE CHINA-MATHEMATICS, 2022, 65 (03) : 443 - 470
  • [19] Gevrey Hypoellipticity for a Class of Kinetic Equations
    Chen, Hua
    Li, Wei-Xi
    Xu, Chao-Jiang
    [J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (04) : 693 - 728
  • [20] Analytic smoothness effect of solutions for spatially homogeneous Landau equation
    Chen, Hua
    Li, Wei-Xi
    Xu, Chao-Jiang
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (01) : 77 - 94
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