3D incompressible flows with small viscosity around distant obstacles

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.14232/EJQTDE.2021.1.31

L. Viana

引用次数: 0

Abstract

In this paper, we analyze the behavior of three-dimensional incompressible flows, with small viscosities ν > 0, in the exterior of material obstacles ΩR = Ω0 + (R, 0, 0), where Ω0 belongs to a class of smooth bounded domains and R > 0 is sufficiently large. Applying techniques developed by Kato, we prove an explicit energy estimate which, in particular, indicates the limiting flow, when both ν → 0 and R → ∞, as that one governed by the Euler equations in the whole space. According to this approach, it is natural to contrast our main result to that one already known in the literature for families of viscous flows in expanding domains.

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三维不可压缩流与小粘度围绕远处障碍物

本文分析了在物质障碍物ΩR = Ω0 + (R, 0,0)外部具有小粘度ν > 0的三维不可压缩流的行为，其中Ω0属于光滑有界区域，且R >足够大。应用Kato所开发的技术，我们证明了一个显式的能量估计，特别是当ν→0和R→∞时，该估计表明整个空间中的极限流是由欧拉方程控制的。根据这种方法，很自然地将我们的主要结果与文献中已知的扩展域中粘性流动族的结果进行对比。

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

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