数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (2): 675-685.doi: 10.1007/s10473-023-0213-5

• • 上一篇    下一篇

ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES*

Xiangkai Lian1, Qiang Tao2,3,†, Zheng-an Yao4   

  1. 1. College of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
    2. College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China;
    3. Shenzhen Key Laboratory of Advanced Machine Learning and Applications, Shenzhen University, Shenzhen 518060, China;
    4. College of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • 收稿日期:2021-12-07 修回日期:2022-02-18 出版日期:2023-03-25 发布日期:2023-04-12
  • 通讯作者: †Qiang Tao, E-mail: taoq060@126.com.
  • 作者简介:Xiangkai Lian, E-mail: lianxk@mail2.sysu.edu.cn; Zheng-an Yao, E-mail: mcsyao@mail.sysu.edu.cn
  • 基金资助:
    This work was partially supported by the National Science Foundation of China (11971320, 11971496), the National Key R $\&$ D Program of China (2020YFA0712500) and the Guangdong Basic and Applied Basic Research Foundation (2020A1515010530).

ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES*

Xiangkai Lian1, Qiang Tao2,3,†, Zheng-an Yao4   

  1. 1. College of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
    2. College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China;
    3. Shenzhen Key Laboratory of Advanced Machine Learning and Applications, Shenzhen University, Shenzhen 518060, China;
    4. College of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2021-12-07 Revised:2022-02-18 Online:2023-03-25 Published:2023-04-12
  • Contact: †Qiang Tao, E-mail: taoq060@126.com.
  • About author:Xiangkai Lian, E-mail: lianxk@mail2.sysu.edu.cn; Zheng-an Yao, E-mail: mcsyao@mail.sysu.edu.cn
  • Supported by:
    This work was partially supported by the National Science Foundation of China (11971320, 11971496), the National Key R $\&$ D Program of China (2020YFA0712500) and the Guangdong Basic and Applied Basic Research Foundation (2020A1515010530).

摘要: In this paper, we study the controllability of compressible Navier-Stokes equations with density dependent viscosities. For when the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda$ is a function of the density, it is proven that the system is exactly locally controllable to a constant target trajectory by using boundary control functions.

关键词: compressible Navier-Stokes equations, controllability, density dependent viscosities

Abstract: In this paper, we study the controllability of compressible Navier-Stokes equations with density dependent viscosities. For when the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda$ is a function of the density, it is proven that the system is exactly locally controllable to a constant target trajectory by using boundary control functions.

Key words: compressible Navier-Stokes equations, controllability, density dependent viscosities