二维纳维-斯托克斯方程的边界层生长机制

IF 2.4 2区数学 Q1 MATHEMATICS Journal of Differential Equations Pub Date : 2024-10-18 DOI:10.1016/j.jde.2024.10.012

Fei Wang , Yichun Zhu

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引用次数: 0

摘要

我们详细描述了不粘性极限问题中边界层的形成。更具体地说，我们证明了边界附近涡度的大小在有限时间内增长到 1/ν，而层的宽度在有限时间内扩展到与ν成正比。事实上，增长时间尺度几乎为 ν。

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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The growth mechanism of boundary layers for the 2D Navier-Stokes equations

We give a detailed description of formation of the boundary layers in the inviscid limit problem. To be more specific, we prove that the magnitude of the vorticity near the boundary is growing to the size of

1 / \sqrt{ν}

and the width of the layer is spreading out to be proportional the

\sqrt{ν}

in a finite time period. In fact, the growth time scaling is almost ν.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics

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