Asymptotic behavior of the two-phase flow around the planar Couette flow in three-dimensional space

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Mathematical Methods in the Applied Sciences Pub Date : 2024-08-26 DOI:10.1002/mma.10423

Deyang Zhang, Houzhi Tang

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Abstract

This paper is concerned with the nonlinear stability of planar Couette flow for the three-dimensional NS-NS equations, which are used to model the motion of two-phase flow. Our result shows that the planar Couette flow is asymptotically stable for the initial perturbations sufficiently small in some Sobolev space if the background velocity and the Reynolds number are sufficiently small. Moreover, it is proved that the solution converges to the stationary state $(ρ_{*}, u_{s}, n_{*}, w_{s})$ at an algebraic time decay rate, and we also give the decay rate of the relative velocity.

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三维空间平面库埃特流周围两相流的渐近行为

本文主要研究用于模拟两相流运动的三维 NS-NS 方程的平面 Couette 流的非线性稳定性。我们的研究结果表明，如果背景速度和雷诺数足够小，平面 Couette 流在某一 Sobolev 空间内对于足够小的初始扰动是渐近稳定的。此外，我们还证明了解以代数时间衰减率收敛于静止状态，并给出了相对速度的衰减率。

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.

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