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Bibliographic Details
Main Authors: Almog, Yaniv, Helffer, Bernard
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2507.19106
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Table of Contents:
  • We consider the stability of a laminar flow $U\in C^4([-1,1])$ in the two-dimensional channel $\mathbb{R} \times[-1,1]$ in the large Reynolds number limit. Assuming that $U$ is strictly monotone but allowing $U^{\prime\prime}$ to vanish, we obtain that if the operator $$ {\mathcal K}_ν=-\frac{d^2}{dx^2}+\frac{U^{\prime\prime}}{U-ν} \,, $$ is strictly positive for all $ν\in\mathbb{R}$ for which $U^{\prime\prime}(U^{-1}(ν))=0$,then $U$ is stable for sufficiently large Reynolds number. This contribution generalizes previous results mostly by allowing long wave perturbations (but much shorter than the Reynolds number).