Two-Dimensional Carreau Law for a Quasi-Newtonian Fluid Flow Through a Thin Domain With a Slightly Rough Boundary

IF 2 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2026-08-09 Epub Date: 2026-05-19 DOI:10.1002/mma.70803

María Anguiano, Francisco Javier Suárez-Grau

引用次数: 0

Abstract

This study investigates the asymptotic behavior of the steady-state quasi-Newtonian Stokes flow with viscosity given by the Carreau law within a thin domain, focusing on the effects of a rough boundary of the domain. Employing asymptotic techniques with respect to the domain's thickness, we rigorously derive the effective nonlinear two-dimensional Reynolds model describing the fluid flow. The mathematical analysis is based on deriving the sharp a priori estimates and proving the compactness results of the rescaled functions together with monotonicity arguments. The resulting limit model incorporates contributions of the oscillating boundary and thus, it could prove useful in the applications involving this lubrication regime.

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本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.