GLOBAL NEWTONIAN LIMIT FOR THE RELATIVISTIC BOLTZMANN EQUATION NEAR VACUUM

被引：45
|
作者：
Strain, Robert M. [1 ]
机构：
[1] Univ Penn, Dept Math, David Rittenhouse Lab, Philadelphia, PA 19104 USA
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 04期
关键词：
relativity; Boltzmann; relativistic Maxwellian; stability; Newtonian limit; collisional kinetic theory; kinetic theory; FOURIER INTEGRAL-OPERATORS; CAUCHY-PROBLEM; ASYMPTOTIC STABILITY; CLASSICAL LIMIT; EXISTENCE PROOF; GAIN-TERM; SYSTEM; COMPACTNESS; UNIQUENESS; BEHAVIOR;
D O I：
10.1137/090762695
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data. Unique global-in-time mild solutions are obtained uniformly in the speed of light parameter c >= 1. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as c -> infinity on arbitrary time intervals [0,T], with convergence rate 1/c(2-epsilon) for any epsilon is an element of (0, 2). This may be the first proof of unique global-in-time validity of the Newtonian limit for a kinetic equation.
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页码：1568 / 1601
页数：34
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