Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

被引：109

作者：

Jia, Hao ^{[1
]}

Sverak, Vladimir ^{[1
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

INVENTIONES MATHEMATICAE | 2014年 / 196卷 / 01期

基金：

美国国家科学基金会;

关键词：

PARTIAL REGULARITY;

D O I：

10.1007/s00222-013-0468-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (-1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.

引用

页码：233 / 265

页数：33

共 25 条

[1]

[Anonymous], 2002, CHAPMAN HALL CRC RES

[2]

Bogovskii M.E., 1980, Theory of cubature formulas and the application of functional analysis to problems of mathematical physics, P5

[3] Fine Properties of Self-Similar Solutions of the Navier-Stokes Equations [J].