Local Energy Weak Solutions for the Navier-Stokes Equations in the Half-Space

被引：25

作者：

Maekawa, Yasunori ^{[1
]}

Miura, Hideyuki ^{[2
]}

Prange, Christophe ^{[3
]}

机构：

[1] Kyoto Univ, Dept Math, Kyoto, Japan

[2] Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo, Japan

[3] Univ Bordeaux, IMB, CNRS, UMR 5251, Bordeaux, France

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2019年 / 367卷 / 02期

关键词：

REGULARITY;

D O I：

10.1007/s00220-019-03344-4

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The purpose of this paper is to prove the existence of global in time local energy weak solutions to the Navier-Stokes equations in the half-space R+3. Such solutions are sometimes called Lemarie-Rieusset solutions in the whole space R3. The main tool in our work is an explicit representation formula for the pressure, which is decomposed into a Helmholtz-Leray part and a harmonic part due to the boundary. We also explain how our result enables to reprove the blow-up of the scale-critical L3(R+3) norm obtained by Barker and Seregin for solutions developing a singularity in finite time.

引用

页码：517 / 580

页数：64

共 35 条

[1] On estimates for the Stokes flow in a space of bounded functions [J].