三维非匀质Navier-Stokes方程的部分正则性  

Partial regularity of the 3-D inhomogeneous Navier-Stokes equations

作　　者：陶涛 王文栋 章志飞[1] 

机构地区：[1]北京大学数学科学学院,北京100871 [2]大连理工大学数学科学学院,大连116024

出　　处：《中国科学：数学》2018年第1期227-244,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11421101和11671067)资助项目

摘　　要：本文首先引进非匀质Navier-Stokes方程恰当弱解的概念.当初始密度接近正常数的情形时,通过结合局部能量不等式、Sobolev嵌入、压力估计和blow up分析技术,本文建立了恰当弱解的内部正则性准则.最后利用内部正则性准则证明了恰当弱解可能奇异点集的一维Hausdorff测度为零.In this paper, we first introduce the concept of suitable weak solutions for the inhomogeneous Navier- Stokes equations. In the case when the initial density is close to a positive constant, by combining local energy inequality, Sobolev embedding, pressure estimate and blow-up analysis, we establish interior regularity criterion of suitable weak solutions. Finally, we show that the 1-D Hausdorff measure of the set of possible singular points of suitable weak solutions vanishes by applying the interior regularity criterion.

关 键 词：非匀质Navier-Stokes方程 部分正则性 内正则性判别 

分 类 号：O175[理学—数学]