LARGE GLOBAL SOLUTIONS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN THREE DIMENSIONS

被引：1

作者：

Zhai, Xiaoping ^{[1
]}

Chen, Yiren ^{[2
]}

LI, Yongsheng ^{[3
]}

机构：

[1] Guangdong Univ Technol, Dept Math, Guangzhou 510520, Peoples R China

[2] Shenzhen Univ, Sch Math & Stat, Shenzhen 518060, Peoples R China

[3] South China Univ Technol, Sch Math, Guangzhou 510640, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2023年 / 43卷 / 01期

关键词：

WELL-POSEDNESS; CRITICAL SPACES; BLOWUP CRITERION; ILL-POSEDNESS; EXISTENCE; STABILITY;

D O I：

10.3934/dcds.2022150

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work concerns the initial value problem for the three dimen-sional compressible Navier-Stokes equations (both isentropic and polytropic). By exploiting the famous Fujita-Kato theorem to the Classical incompressible Navier-Stokes equations, we prove the existence of global-in-time unique solu-tions under as weak as possible smallness conditions in the scaling invariant spaces. In particular, our results improve the classical theorems obtained by Danchin [Invent. Math., 141, 579-614, 2000] and Danchin [Arch. Ration. Mech. Anal., 160, 1-39, 2001].

引用

页码：309 / 337

页数：29

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