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

doi:10.1007/s10473-023-0213-5

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

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

Xiangkai Lian¹, Qiang Tao^2,3,†, Zheng-an Yao⁴

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 Tao^2,3,†, Zheng-an Yao⁴

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/Abstract

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

Xiangkai Lian, Qiang Tao, Zheng-an Yao. ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES^*[J]. 数学物理学报(英文版), 2023, 43(2): 675-685.

Xiangkai Lian, Qiang Tao, Zheng-an Yao. ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES^*[J]. Acta mathematica scientia,Series B, 2023, 43(2): 675-685.

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

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

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