GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

doi:10.1007/s10473-022-0523-z

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (5): 2131-2148.doi: 10.1007/s10473-022-0523-z

• 论文 • 上一篇

GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

Jinlu LI^1,2, Zhaoyang YIN^2,3, Xiaoping ZHAI^4,5

1. School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, 341000, China;
2. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China;
3. Faculty of Information Technology, Macau University of Science and Technology, Macau, China;
4. Department of Mathematics, Guangdong University of Technology, Guangzhou, 510520, China;
5. School of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

收稿日期:2020-03-10 修回日期:2022-05-05 发布日期:2022-11-02
通讯作者: Xiaoping Zhai,E-mail:pingxiaozhai@163.com E-mail:pingxiaozhai@163.com
基金资助:
The first author was supported by the National Natural Science Foundation of China (11801090 and 12161004) and Jiangxi Provincial Natural Science Foundation, China (20212BAB211004). The second author was supported by the National Natural Science Foundation of China (12171493). The third author was supported by the National Natural Science Foundation of China (11601533), Guangdong Provincial Natural Science Foundation, China (2022A1515011977), and the Science and Technology Program of Shenzhen under grant 20200806104726001.

GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

Jinlu LI^1,2, Zhaoyang YIN^2,3, Xiaoping ZHAI^4,5

1. School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, 341000, China;
2. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China;
3. Faculty of Information Technology, Macau University of Science and Technology, Macau, China;
4. Department of Mathematics, Guangdong University of Technology, Guangzhou, 510520, China;
5. School of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

Received:2020-03-10 Revised:2022-05-05 Published:2022-11-02
Contact: Xiaoping Zhai,E-mail:pingxiaozhai@163.com E-mail:pingxiaozhai@163.com
Supported by:
The first author was supported by the National Natural Science Foundation of China (11801090 and 12161004) and Jiangxi Provincial Natural Science Foundation, China (20212BAB211004). The second author was supported by the National Natural Science Foundation of China (12171493). The third author was supported by the National Natural Science Foundation of China (11601533), Guangdong Provincial Natural Science Foundation, China (2022A1515011977), and the Science and Technology Program of Shenzhen under grant 20200806104726001.

摘要/Abstract

摘要： We are concerned with the Cauchy problem regarding the full compressible Navier-Stokes equations in $\mathbb{R}^d$ (d = 2, 3). By exploiting the intrinsic structure of the equations and using harmonic analysis tools (especially the Littlewood-Paley theory), we prove the global solutions to this system with small initial data restricted in the Sobolev spaces. Moreover, the initial temperature may vanish at infinity.

关键词: compressible Navier-Stokes equations, global well-posedness, Friedrich’s method, compactness arguments

Abstract: We are concerned with the Cauchy problem regarding the full compressible Navier-Stokes equations in $\mathbb{R}^d$ (d = 2, 3). By exploiting the intrinsic structure of the equations and using harmonic analysis tools (especially the Littlewood-Paley theory), we prove the global solutions to this system with small initial data restricted in the Sobolev spaces. Moreover, the initial temperature may vanish at infinity.

Key words: compressible Navier-Stokes equations, global well-posedness, Friedrich’s method, compactness arguments

中图分类号:

35Q35

Jinlu LI, Zhaoyang YIN, Xiaoping ZHAI. GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS[J]. 数学物理学报(英文版), 2022, 42(5): 2131-2148.

Jinlu LI, Zhaoyang YIN, Xiaoping ZHAI. GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS[J]. Acta mathematica scientia,Series B, 2022, 42(5): 2131-2148.

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GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

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