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

页码：327 / 381

页数：55

共 50 条

[21] Well-posedness and global existence for the Novikov equation
Wu, Xinglong
Yin, Zhaoyang
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2012, 11 (03) : 707 - 727
[22] Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff
Alexandre, Radjesvarane
Morimoto, Y.
Ukai, S.
Xu, Chao-Jiang
Yang, T.
COMPTES RENDUS MATHEMATIQUE, 2010, 348 (15-16) : 867 - 871
[23] Small Data Global Well-Posedness and Scattering for the Inhomogeneous Nonlinear Schrodinger Equation in Hs(Rn)
An, JinMyong
Kim, JinMyong
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2021, 40 (04): : 453 - 475
[24] Global Well-Posedness for the Massive Maxwell–Klein–Gordon Equation with Small Critical Sobolev Data
Cristian Gavrus
Annals of PDE, 2019, 5
[25] Local and global well-posedness for the Ostrovsky equation
Linares, F
Milanés, A
JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 222 (02) : 325 - 340
[26] Local well-posedness for periodic Benjamin equation with small initial data
Shi, Shaoguang
Li, Junfeng
BOUNDARY VALUE PROBLEMS, 2015, : 1 - 15
[27] NONNEGATIVITY AND WELL-POSEDNESS OF THE REGULAR SOLUTION OF THE MAGNETIZED BOLTZMANN EQUATION
Dongo, David
Djiofack, Francis Etienne
REPORTS ON MATHEMATICAL PHYSICS, 2020, 85 (02) : 193 - 208
[28] Local well-posedness for periodic Benjamin equation with small initial data
Shaoguang Shi
Junfeng Li
Boundary Value Problems, 2015
[29] Oscillatory integral estimates and global well-posedness for the 2D Boussinesq equation
Luiz Gustavo Farah
Frederic Rousset
Nikolay Tzvetkov
Bulletin of the Brazilian Mathematical Society, New Series, 2012, 43 : 655 - 679
[30] Oscillatory integral estimates and global well-posedness for the 2D Boussinesq equation
Farah, Luiz Gustavo
Rousset, Frederic
Tzvetkov, Nikolay
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2012, 43 (04): : 655 - 679

← 1 2 3 4 5 →