Global solutions to 3D incompressible Navier-Stokes equations with some large initial data

被引：0

作者：

Yu, Yanghai ^{[1
]}

Li, Jinlu ^{[2
]}

Yin, Zhaoyang ^{[3
]}

机构：

[1] Anhui Normal Univ, Sch Math & Stat, Wuhu 241002, Peoples R China

[2] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Peoples R China

[3] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2022年 / 129卷

基金：

中国国家自然科学基金;

关键词：

Incompressible Navier-Stokes; equations; Large solution; WELL-POSEDNESS; WELLPOSEDNESS;

D O I：

10.1016/j.aml.2022.107954

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we derive a new smallness hypothesis of initial data for the three-dimensional incompressible Navier-Stokes equations. More precisely, we prove that if (parallel to u(0)(1) + u(0)(2)parallel to(3/p-1)(<(B) over dot>)(p,1) + parallel to u(0)(3)parallel to(3/p-1)(<(B) over dot>)(p,1)) x exp(C(parallel to u(0)parallel to(2)(-1)(<(B) over dot>)(infinity,1) + parallel to u(0)parallel to(-1)(<(B) over dot>)(infinity,1))) is small enough, the Navier-Stokes equations have a unique global solution. As an application, we construct two examples of initial data satisfying the smallness condition, but whose (-1)((B) over dot>)(infinity,infinity)(R-3) norm can be arbitrarily large. (C) 2022 Elsevier Ltd. All rights reserved.

引用

页数：8

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