Gevrey-Class-3 Regularity of the Linearised Hyperbolic Prandtl System on a Strip

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-01 DOI:10.1007/s00021-023-00821-8

Francesco De Anna, Joshua Kortum, Stefano Scrobogna

引用次数: 2

Abstract

In the present paper, we address a physically-meaningful extension of the linearised Prandtl equations around a shear flow. Without any structural assumption, it is well-known that the optimal regularity of Prandtl is given by the class Gevrey 2 along the horizontal direction. The goal of this paper is to overcome this barrier, by dealing with the linearisation of the so-called hyperbolic Prandtl equations in a strip domain. We prove that the local well-posedness around a general shear flow \(U_{\textrm{sh}}\in W^{3, \infty }(0,1)\) holds true, with solutions that are Gevrey class 3 in the horizontal direction.

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条上线性化双曲Prandtl系统的gevrey -3类正则性

在本文中，我们讨论了围绕剪切流的线性化普朗特方程的物理意义上的扩展。众所周知，在没有任何结构假设的情况下，Prandtl的最优正则性是由Gevrey 2类沿水平方向给出的。本文的目标是克服这一障碍，通过处理所谓的双曲普朗特方程的线性化在条形域。我们证明了一般剪切流\(U_{\textrm{sh}}\in W^{3, \infty }(0,1)\)周围的局部适定性成立，且解在水平方向上为Gevrey类3。

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.