条上线性化双曲Prandtl系统的gevrey -3类正则性

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2023-09-01 DOI:10.1007/s00021-023-00821-8

Francesco De Anna, Joshua Kortum, Stefano Scrobogna

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引用次数: 2

摘要

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

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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来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.