Asymptotic analysis of a micropolar fluid flow in a thin domain with a free and rough boundary
type: Item
instance of: scholarly article
zbMATH Open document ID: 1259.35164
DOI: 10.1137/110837772
author: Mahdi Boukrouche
author: Laetitia Paoli
published in: SIAM Journal on Mathematical Analysis
publication date: 2012-08-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1309.4875
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 76D08
Mathematics Subject Classification ID: 76M50
zbMATH DE Number: 6070885
zbMATH Keywords: lubrication
zbMATH Keywords: micropolar fluid
zbMATH Keywords: free and rough boundary
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: two-scale convergence
zbMATH Keywords: Reynolds equations
MaRDI profile type: Publication
OpenAlex ID: W2023273917
arXiv ID: 1309.4875
title: Asymptotic analysis of a micropolar fluid flow in a thin domain with a free and rough boundary
review text: The lubrication problem is considered as micropolar fluid flow in a two-dimensional domain with free boundary of small thinness and roughness, described by a PDEs system with respect to the velocity field of the fluid \(u^{\varepsilon}=(u_{1}^{\varepsilon},u_{2}^{\varepsilon}),\) the pressure \(p^{\varepsilon}\) and the angular velocity \(\omega^{\varepsilon}\) of the microrotations of the particles. It consists of the equilibrium equations for momentum, mass and moment of momentum and is considered in the space-time domain \((0,T)\times\Omega^{\varepsilon}\), \(\Omega^{\varepsilon}=\{z=(z_{1},z_{2})\in{\mathbb{R}^{2}}\), \(0<z_{1}<L\), \(0<z_{2}<\varepsilon h^{\varepsilon}(z_{1})\}\), \(h^{\varepsilon}(z_{1})=h(z_{1}\), \(\frac{z_{1}}{\varepsilon})\). Here the form of \(\Omega^{\varepsilon}\) is originated from the important fields of lubrication theory and applications in the mechanical and electromechanical industries.NEWLINENEWLINEIn the relevant functional spaces, the existence and uniqueness of a weak solution to the PDEs system is proved. Then a priori estimates for the velocity, microrotation and pressure independently on \(\varepsilon\) are established. The limit problem when \(\varepsilon\) tends to zero is studied.
reviewed by: Svetlana A. Grishina
description: scientific article; zbMATH DE number 6070885