Well-Posedness and Singularity Formation for the Kolmogorov Two-Equation Model of Turbulence in 1-D

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-06 DOI:10.1007/s10884-023-10326-7

Francesco Fanelli, Rafael Granero-Belinchón

引用次数: 4

Abstract

We study the Kolomogorov two-equation model of turbulence in one space dimension. Two are the main results of the paper. First of all, we establish a local well-posedness theory in Sobolev spaces even in the case of vanishing mean turbulent kinetic energy. Then, we show that there are smooth solutions which blow up in finite time. To the best of our knowledge, these results are the first establishing the well-posedness of the system for vanishing initial data and the occurence of finite time singularities for the model under study.

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一维湍流Kolmogorov双方程模型的适定性和奇点形成

研究了一维空间湍流的Kolomogorov双方程模型。两个是本文的主要结果。首先，我们建立了Sobolev空间中平均湍流动能消失情况下的局部适定性理论。然后，我们证明了存在在有限时间内爆炸的光滑解。据我们所知，这些结果是第一次建立了系统对消失的初始数据和有限时间奇点的存在的适定性。

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.