Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (5): 2131-2148.doi: 10.1007/s10473-022-0523-z

• Articles • Previous Articles    

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

Jinlu LI1,2, Zhaoyang YIN2,3, Xiaoping ZHAI4,5   

  1. 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.

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

CLC Number: 

  • 35Q35
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