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

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• 作者：Xiuli Zhu ; Zhonghai Xu ; Huapeng Li
• 关键词：Incompressible micropolar fluid ; Convergence rates ; Boundary layer
• 刊名：Acta Applicandae Mathematicae
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：147
• 期：1
• 页码：113-136
• 全文大小：
• 刊物主题：Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9036
• 卷排序：147

文摘

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.