一维湍流Kolmogorov双方程模型的适定性和奇点形成

IF 1.4 4区数学 Q1 MATHEMATICS

Journal of Dynamics and Differential Equations Pub Date : 2023-11-06 DOI:10.1007/s10884-023-10326-7

Francesco Fanelli, Rafael Granero-Belinchón

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引用次数: 4

摘要

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

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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来源期刊

Journal of Dynamics and Differential Equations 数学-数学

CiteScore

3.30

自引率

7.70%

发文量

116

审稿时长

>12 weeks

期刊介绍： Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.