VANISHING VISCOSITY LIMIT FOR THE 3D INCOMPRESSIBLE MICROPOLAR EQUATIONS IN A BOUNDED DOMAIN*

doi:10.1007/s10473-023-0224-2

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (2): 959-974.doi: 10.1007/s10473-023-0224-2

VANISHING VISCOSITY LIMIT FOR THE 3D INCOMPRESSIBLE MICROPOLAR EQUATIONS IN A BOUNDED DOMAIN^*

Yangyang, Chu, Yuelong Xiao^†

Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

收稿日期:2021-12-21 修回日期:2022-02-24 出版日期:2023-03-25 发布日期:2023-04-12
通讯作者: †Yuelong Xiao, E-mail: xyl@xtu.edu.cn.
作者简介:Yangyang Chu,E-mail: cyy@smail.xtu.edu.cn
基金资助:
This work was supported by the NSFC (11871412) and the Postgraduate Scientific Research Innovation Project of Xiangtan University (XDCX2020B088).

VANISHING VISCOSITY LIMIT FOR THE 3D INCOMPRESSIBLE MICROPOLAR EQUATIONS IN A BOUNDED DOMAIN^*

Yangyang, Chu, Yuelong Xiao^†

Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Received:2021-12-21 Revised:2022-02-24 Online:2023-03-25 Published:2023-04-12
Contact: †Yuelong Xiao, E-mail: xyl@xtu.edu.cn.
About author:Yangyang Chu,E-mail: cyy@smail.xtu.edu.cn
Supported by:
This work was supported by the NSFC (11871412) and the Postgraduate Scientific Research Innovation Project of Xiangtan University (XDCX2020B088).

摘要/Abstract

摘要： In this paper, we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary conditions. It is shown that there exist global weak solutions of the micropolar equations in a general bounded smooth domain. In particular, we establish the uniform estimate of the strong solutions for when the boundary is flat. Furthermore, we obtain the rate of convergence of viscosity solutions to the inviscid solutions as the viscosities tend to zero (i.e., $(\varepsilon,\chi,\gamma,\kappa)\to 0$).

关键词: incompressible micropolar equations, initial- and boundary-value problem, vanishing viscosity limit

Abstract: In this paper, we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary conditions. It is shown that there exist global weak solutions of the micropolar equations in a general bounded smooth domain. In particular, we establish the uniform estimate of the strong solutions for when the boundary is flat. Furthermore, we obtain the rate of convergence of viscosity solutions to the inviscid solutions as the viscosities tend to zero (i.e., $(\varepsilon,\chi,\gamma,\kappa)\to 0$).

Key words: incompressible micropolar equations, initial- and boundary-value problem, vanishing viscosity limit

Yangyang, Chu, Yuelong Xiao. VANISHING VISCOSITY LIMIT FOR THE 3D INCOMPRESSIBLE MICROPOLAR EQUATIONS IN A BOUNDED DOMAIN^*[J]. 数学物理学报(英文版), 2023, 43(2): 959-974.

Yangyang, Chu, Yuelong Xiao. VANISHING VISCOSITY LIMIT FOR THE 3D INCOMPRESSIBLE MICROPOLAR EQUATIONS IN A BOUNDED DOMAIN^*[J]. Acta mathematica scientia,Series B, 2023, 43(2): 959-974.

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VANISHING VISCOSITY LIMIT FOR THE 3D INCOMPRESSIBLE MICROPOLAR EQUATIONS IN A BOUNDED DOMAIN^*

VANISHING VISCOSITY LIMIT FOR THE 3D INCOMPRESSIBLE MICROPOLAR EQUATIONS IN A BOUNDED DOMAIN^*

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