Stability for the 2D Micropolar equations with partial dissipation near Couette flow

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-18 DOI:10.4310/cms.2024.v22.n6.a4

Xueting Jin, Quansen Jiu

引用次数: 0

Abstract

In this paper, we will apply the Fourier multiplier method to explore the stability for the 2D micropolar equations with partial dissipation near Couette flow. The difficulty will be encountered due to the facts that one order derivative of the microtation appears on the right term of velocity equations and that the velocity equations only have vertical dissipation. To overcome the difficulty, we will make use of a Fourier multiplier to grasp the enhanced dissipation created by the special structure $y\partial_x-\nu\partial_{y}^2$ and obtain some new and higher-order estimates of the solution in an elegant way. Also, a time-dependent elliptic operator $\Lambda_t^b$ which commutes with linear part of the equations will be used to make our proof more clear.

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具有部分耗散的近库特流二维微波方程的稳定性

在本文中，我们将应用傅立叶乘法器方法来探索具有部分耗散的二维微扰方程在库尔特流附近的稳定性。由于微动的一阶导数出现在速度方程的右项上，而且速度方程只有垂直耗散，因此会遇到困难。为了克服这一困难，我们将利用傅立叶乘法器来掌握特殊结构 $y\partial_x-\nu\partial_{y}^2$ 所产生的增强耗散，并以一种优雅的方式获得一些新的高阶估计解。此外，我们还将使用与方程线性部分相乘的时变椭圆算子 $\Lambda_t^b$ 来使我们的证明更加清晰。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.