In lubrication problems, which concern thin film flow, cavitation has been considered as a fundamental element to correctly describe the characteristics of lubricated mechanisms. Here, the well-posedness of a cavitation model that can explain the interaction between viscous effects and micro-bubbles of gas is studied. This cavitation model consists of a coupled problem between the compressible Reynolds partial differential equation (PDE) (that describes the flow) and the Rayleigh–Plesset ordinary differential equation (that describes micro-bubbles evolution). A simplified form without bubbles convection is studied here. This coupled model seems never to be studied before from its mathematical aspects. Local times existence results are proved and stability theorems are obtained based on the continuity of the spectrum for bounded linear operators. Numerical results are presented to illustrate these theoretical results.

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关于薄膜润滑中包含气泡的空化模型：第一次数学分析

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要素。在这里，研究了可以解释粘性效应和气体微气泡之间相互作用的空化模型的适定性。该空化模型由可压缩雷诺偏微分方程 (PDE)（描述流动）和 Rayleigh-Plesset 常微分方程（描述微气泡演化）之间的耦合问题组成。这里研究了一种没有气泡对流的简化形式。这种耦合模型似乎从未从其数学方面进行过研究。基于有界线性算子谱的连续性，证明了局部时间存在性结果，得到了稳定性定理。