LOCAL EXISTENCE WITH MILD REGULARITY FOR THE BOLTZMANN EQUATION

被引：45

作者：

Alexandre, Radjesvarane ^{[1
,2
]}

Morimoto, Yoshinori ^{[3
]}

Ukai, Seiji

Xu, Chao-Jiang ^{[4
,5
]}

Yang, Tong ^{[6
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] French Naval Acad Brest Lanveoc, IRENAV Res Inst, F-29290 Brest, France

[3] Kyoto Univ, Grad Sch Human & Environm Studies, Kyoto 6068501, Japan

[4] Univ Rouen, CNRS, UMR 6085, F-76801 St Etienne, France

[5] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[6] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

来源：

基金：

美国国家科学基金会;

关键词：

Boltzmann equation; energy estimates; existence of solution; fractional derivatives; LONG-RANGE INTERACTIONS; ANGULAR CUTOFF; WHOLE SPACE; GLOBAL EXISTENCE; BOUNDED SOLUTIONS;

D O I：

10.3934/krm.2013.6.1011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Without Grad's angular cutoff assumption, the local existence of classical solutions to the Boltzmann equation is studied. There are two new improvements: the index of Sobolev spaces for the solution is related to the parameter of the angular singularity; moreover, we do not assume that the initial data is close to a global equilibrium. Using the energy method, one important step in the analysis is the study of fractional derivatives of the collision operator and related commutators.

引用

页码：1011 / 1041

页数：31

共 26 条

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