On nonlinear instability of Prandtl's boundary layers: The case of Rayleigh's stable shear flows

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Emmanuel Grenier , Toan T. Nguyen
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引用次数: 0

Abstract

In 1904, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of Navier Stokes equations near a boundary as the viscosity goes to 0. His Ansatz has later been justified for analytic data by R.E. Caflisch and M. Sammartino. In this paper, we prove that his expansion is false, up to O(ν1/4) order terms in L norm, in the case of solutions with Sobolev regularity, even in cases where the Prandlt's equation is well posed in Sobolev spaces.

In addition, we also prove that monotonic boundary layer profiles, which are stable when ν=0, are nonlinearly unstable when ν>0, provided ν is small enough, up to O(ν1/4) terms in L norm.

论普朗特边界层的非线性不稳定性:瑞利稳定剪切流的情况
1904 年,普朗特提出了著名的边界层,以描述纳维-斯托克斯方程的解在边界附近粘度为 0 时的行为。在本文中,我们证明在具有索博廖夫正则性的解的情况下,即使普朗特方程在索博廖夫空间中假设良好,他的扩展也是错误的,最多只能扩展到规范的阶次项。
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
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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