Abstract
This paper deals with an initial-boundary value problem to the two-dimensional equations of incompressible micropolar fluids. We first prove that as the angular and micro-rotational viscosities go to zero (i.e., \({\gamma, \zeta \to 0}\)), the solution converges to a global weak solution of the original equations with zero angular and micro-rotational viscosities. Convergence rates are also obtained. Then, we study the boundary effects and prove that a boundary-layer thickness is of the value \({\delta(\gamma) = \gamma^\alpha}\) with \({\alpha \in (0, 1/2)}\) , provided \({\lim_{\gamma \to 0} \zeta \gamma^{1/2} < \infty}\) .
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This work was partially supported by NNSFC (Grant nos. 10971171 and 11271306), the Fundamental Research Funds for the Central Universities (Grant no. 2012121005), the Natural Science Foundation of Fujian Province of China (Grant no. 2010J05011), and the Independent Innovation Foundation of Shandong University (No. 2013ZRQP001).
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Chen, M., Xu, X. & Zhang, J. The zero limits of angular and micro-rotational viscosities for the two-dimensional micropolar fluid equations with boundary effect. Z. Angew. Math. Phys. 65, 687–710 (2014). https://doi.org/10.1007/s00033-013-0345-x
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DOI: https://doi.org/10.1007/s00033-013-0345-x