Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (2): 959-974.doi: 10.1007/s10473-023-0224-2

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

Yangyang, Chu, Yuelong Xiao   

  1. 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).

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

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