A cheap Caffarelli-Kohn-Nirenberg inequality for the Navier-Stokes equation with hyper-dissipation

被引：129

作者：

Katz, NH ^{[1
]}

Pavlovic, N

机构：

[1] Washington Univ, Dept Math, St Louis, MO 63130 USA

[2] Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2002年 / 12卷 / 02期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1007/s00039-002-8250-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for the Navier-Stokes equation with dissipation (-Delta)(alpha), where 1 < alpha < 5/4, and smooth initial data, the Hausdorff dimension of the singular set at time of first blow up is at most 5 - 4alpha. This unifies two directions from which one might approach the problem of global solvability, though it provides no direct progress on either.

引用

页码：355 / 379

页数：25

共 11 条

[1]

BONY JM, 1981, ANN SCI ECOLE NORM S, V14, P209

[2] PARTIAL REGULARITY OF SUITABLE WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS [J].