The zero limits of angular and micro-rotational viscosities for the two-dimensional micropolar fluid equations with boundary effect

Autor: Mingtao Chen, Jianwen Zhang, Xinying Xu
Rok vydání: 2013
Předmět:
Zdroj: Zeitschrift für angewandte Mathematik und Physik. 65:687-710
ISSN: 1420-9039
0044-2275
Popis: 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 $${\lim_{\gamma \to 0} \zeta \gamma^{1/2} < \infty}$$ .
Databáze: OpenAIRE
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