About a cavitation model including bubbles in thin film lubrication taking convection into account

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2022-01-18 DOI:10.1090/qam/1609

G. Bayada, I. Ciuperca

引用次数: 0

Abstract

In lubrication problems, which concern thin film flow, cavitation has been considered as a fundamental element to correctly describe the characteristics of lubricated mechanisms. This cavitation model consists of a coupled problem between the compressible Reynolds PDE (that describes the flow) and the Rayleigh-Plesset ODE (that describes micro-bubbles evolution). Very few theoretical results exist in the mathematical literature about such couple problems. A complete form including bubbles convection is studied here. Local times existence results are proved based on the semi group theory. Stability theorems are obtained in a particular case.

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关于考虑对流的薄膜润滑中含气泡的空化模型

在涉及薄膜流动的润滑问题中，空化被认为是正确描述润滑机构特性的基本因素。该空化模型由可压缩Reynolds PDE（描述流动）和Rayleigh Plesset ODE（描述微气泡演化）之间的耦合问题组成。数学文献中很少有关于这类耦合问题的理论结果。本文研究了一个包含气泡对流的完整形式。基于半群理论证明了局部时间存在性的结果。稳定性定理是在一个特殊情况下得到的。

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

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.