Small Data Global Well-Posedness for a Boltzmann Equation via Bilinear Spacetime Estimates

被引：6
|
作者：
Chen, Thomas [1 ]
Denlinger, Ryan [1 ]
Pavlovic, Natasa [1 ]
机构：
[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2021年 / 240卷 / 01期
关键词：
CLASSICAL-SOLUTIONS; EXISTENCE; SCATTERING; UNIQUENESS;
D O I：
10.1007/s00205-021-01613-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide a new analysis of the Boltzmann equation with a constant collision kernel in two space dimensions. The scaling-critical Lebesgue space is L-2x,v(2); we prove the global well-posedness and a version of scattering, assuming that the data f(0) is sufficiently smooth and localized, and the L-x,v(2) norm of f(0) is sufficiently small. The proof relies upon a new scaling-critical bilinear spacetime estimate for the collision "gain" term in Boltzmann's equation, combined with a novel application of the Kaniel-Shinbrot iteration.
引用
收藏
页码：327 / 381
页数：55
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