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The control of the boundary layer for the micropolar fluid equations with zero limits of angular and microrotational viscosities

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Abstract

In this paper, we consider an initial-boundary value problem to the two-dimensional incompressible micropolar fluid equations. Our main purpose is to study the boundary layer effects, and especially, we pay more attention to control the boundary layer as the angular and microrotational viscosities go to zero. It is shown that the boundary layer thickness can be controlled by the derivative of the boundary temperature with respect to time. As a matter of fact, the relationship between the boundary layer thickness (\(O(\gamma ^\beta )\)) and the time derivative of the boundary temperature can be found in (1.13). Meanwhile, we generalize the conclusion of Reference Chen et al. (Z Angew Math Phys 65:687–710, 2014).

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Authors and Affiliations

  1. College of Science, Northeast Electric Power University, Jilin, 132013, Jilin, People’s Republic of China

    Zhonghai Xu, Xiuli Zhu, Huapeng Li & Dapeng Zhang

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  1. Zhonghai Xu
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  2. Xiuli Zhu
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  3. Huapeng Li
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  4. Dapeng Zhang
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Corresponding author

Correspondence to Xiuli Zhu.

Additional information

This work was supported by Science and Technology Developing Project of Jilin Province of China (Grant Nos. 20150101002JC, 20156405), Scientific Research Fund of Jilin Provincial Education of China (Grant No. 2016(81), JJKH20170095KJ) and NSFC (Grant No. 11626055).

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Xu, Z., Zhu, X., Li, H. et al. The control of the boundary layer for the micropolar fluid equations with zero limits of angular and microrotational viscosities. Z. Angew. Math. Phys. 68, 60 (2017). https://doi.org/10.1007/s00033-017-0804-x

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  • DOI: https://doi.org/10.1007/s00033-017-0804-x

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