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The Boundary Effects and Zero Angular and Micro-rotational Viscosities Limits of the Micropolar Fluid Equations

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Abstract

In this paper, we consider an initial-value problem to the two-dimensional incompressible micropolar fluid equations. Our main purpose is to study the boundary layer effects as the angular and micro-rotational viscosities go to zero. It is also shown that the boundary layer thickness is of the order \(O(\gamma^{\beta })\) with \((0<\beta <\frac{2}{3})\). In contrast with Chen et al. (Z. Angew. Math. Phys. 65:687–710, 2014), the BL-thickness we got is thinner than that in Chen et al. (Z. Angew. Math. Phys. 65:687–710, 2014). In addition, the convergence rates are also improved.

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Authors and Affiliations

  1. College of Science, Northeast Dianli University, Jilin, Jilin, 132013, P.R. China

    Xiuli Zhu, Zhonghai Xu & Huapeng Li

Authors
  1. Xiuli Zhu
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  2. Zhonghai Xu
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  3. Huapeng Li
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Corresponding authors

Correspondence to Xiuli Zhu or Zhonghai Xu.

Additional information

This work was partially supported by the Science and Technology Developing Project of Jilin Province of China (Grant no. 20150101002JC), the Science and Technology Developing Project of Jilin city Jilin Province of China (Grant no. 20156405).

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Zhu, X., Xu, Z. & Li, H. The Boundary Effects and Zero Angular and Micro-rotational Viscosities Limits of the Micropolar Fluid Equations. Acta Appl Math 147, 113–136 (2017). https://doi.org/10.1007/s10440-016-0071-4

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  • DOI: https://doi.org/10.1007/s10440-016-0071-4

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