强迫Navier-Stokes方程的Onstager临界解

IF 1 3区数学 Q1 MATHEMATICS

Communications on Pure and Applied Analysis Pub Date : 2022-12-16 DOI:10.3934/cpaa.2023071

Elia Brué, Maria Colombo, Gianluca Crippa, Camillo De Lellis, M. Sorella

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引用次数: 9

摘要

对于任意固定的$\varepsilon> $，我们通过建立具有消失黏度的强制3d-Navier-Stokes方程的新解来肯定地回答[BDL22，问题2.4]，该方程表现出异常耗散并且在空间$L_t^ 3c_x ^{1/3 - \varepsilon}$中具有均匀界。我们的构造结合了[BDL22]和[CCS22]的思想。

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Onsager critical solutions of the forced Navier-Stokes equations

We answer positively to [BDL22, Question 2.4] by building new examples of solutions to the forced 3d-Navier-Stokes equations with vanishing viscosity, which exhibit anomalous dissipation and which enjoy uniform bounds in the space $L_t^3 C_x^{1/3 - \varepsilon}$, for any fixed $\varepsilon>0$. Our construction combines ideas of [BDL22] and [CCS22].

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来源期刊

Communications on Pure and Applied Analysis 数学-数学

CiteScore

1.90

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal''s highest standard and closest link to the scientific communities.