单调粘性边界层中非线性不稳定性的出现

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Mathematical Analysis Pub Date : 2024-05-31 DOI:10.1137/22m1505773

D. Bian, E. Grenier

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷，第 3 期，第 3703-3719 页，2024 年 6 月。摘要本文研究了边界附近 Navier-Stokes 方程剪切层剖面的非线性稳定性。更确切地说，我们研究了立方相互作用对线性不稳定性增长的影响。在指数剖面的情况下，我们发现非线性抑制了线性不稳定性。因此，我们猜想，小扰动会一直增长，直到达到[math]的量级，在临界层中形成靠近边界的小滚动。这一猜想的数学证明尚未完成。

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Onset of Nonlinear Instabilities in Monotonic Viscous Boundary Layers

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3703-3719, June 2024.
Abstract. In this paper, we study the nonlinear stability of a shear layer profile for Navier–Stokes equations near a boundary. More precisely, we investigate the effect of cubic interactions on the growth of the linear instability. In the case of the exponential profile, we obtain that the nonlinearity tames the linear instability. We thus conjecture that small perturbations grow until they reach a magnitude [math] only, forming small rolls in the critical layer near the boundary. The mathematical proof of this conjecture is open.

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.