REGULARITY ANALYSIS FOR SYSTEMS OF REACTION-DIFFUSION EQUATIONS

被引：0

作者：

Goudon, Thierry ^{[1
,2
]}

Vasseur, Alexis ^{[3
]}

机构：

[1] Project Team SIMPAF INRIA Lille Nord Europe, F-59650 Villeneuve Dascq, France

[2] Labo Paul Painleve CNRS USTLille, F-59650 Villeneuve Dascq, France

[3] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2010年 / 43卷 / 01期

基金：

美国国家科学基金会;

关键词：

NAVIER-STOKES EQUATIONS; GLOBAL EXISTENCE; ENTROPY METHODS; WEAK SOLUTIONS; BLOW-UP; PROOF; DECAY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to the study of the regularity of solutions to some systems of reaction diffusion equations. In particular, we show the global boundedness and regularity of the solutions in one and two dimensions. In addition, we discuss the Hausdorff dimension of the set of singularities in higher dimensions. Our approach is inspired by De Giorgi's method for elliptic regularity with rough coefficients. The proof uses the specific structure of the system to be considered and is not a mere adaptation of scalar techniques; in particular the natural entropy of the system plays a crucial role in the analysis.

引用

页码：117 / 142

页数：26

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