The Landau equation in a periodic box

被引:250
作者
Guo, Y [1 ]
机构
[1] Brown Univ, Div Appl Math, Lefshitz Ctr Dynam Syst, Providence, RI 02912 USA
关键词
D O I
10.1007/s00220-002-0729-9
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The Landau equation, which was proposed by Landau in 1936, is a fundamental equation to describe collisions among charged particles interacting with their Coulombic force. In this article, global in time classical solutions near Maxwellians are constructed for the Landau equation in a periodic box. Our result also covers a class of generalized Landau equations, which describes grazing collisions in a dilute gas.
引用
收藏
页码:391 / 434
页数:44
相关论文
共 14 条
[1]   ON THE CONNECTION BETWEEN A SOLUTION OF THE BOLTZMANN-EQUATION AND A SOLUTION OF THE LANDAU-FOKKER-PLANCK EQUATION [J].
ARSENEV, AA ;
BURYAK, OE .
MATHEMATICS OF THE USSR-SBORNIK, 1991, 69 (02) :465-478
[2]  
Cercignani C, 1988, BOLTZMANN EQUATION I
[3]  
Cercignani C, 1994, MATH THEORY DILUTE G
[4]   Dispersion relations for the linearized Fokker-Planck equation [J].
Degond, P ;
Lemou, M .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1997, 138 (02) :137-167
[5]   On the spatially homogeneous landau equation for hard potentials - Part I: Existence, uniqueness and smoothness [J].
Desvillettes, L ;
Villani, C .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2000, 25 (1-2) :179-259
[6]   ABOUT THE REGULARIZING PROPERTIES OF THE NON-CUT-OFF KAC EQUATION [J].
DESVILLETTES, L .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1995, 168 (02) :417-440
[7]   GLOBAL WEAK SOLUTIONS OF VLASOV-MAXWELL SYSTEMS [J].
DIPERNA, RJ ;
LIONS, PL .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (06) :729-757
[8]  
GLASSEY R., 1996, CAUCHY PROBLEMS KINE
[9]   The Vlasov-Poisson-Boltzmann system near Maxwellians [J].
Guo, Y .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2002, 55 (09) :1104-1135
[10]  
GUO Y, 2001, INVERSE POWER LAW AN