Work

Eigenvalues of the linearized Navier-Stokes operator near locally Couette laminar flows

Year: 2026

Type: preprint

Abstract: We consider the spectrum of the Orr-Sommerfeld operator, which is obtained from the linearized Navier-Stokes (LNS) operator near a laminar flow in an infinite two-dimensional channel in the large Reynolds number limit. For a rather general class of laminar flows, which behave locally near the boundary like a Couette flow and are bounded from below (above) by a linear increasing (decreasing) function, we show that there exists an eigenvalue of the LNS operator which coincides, to leading order, with the eigenvalue of LNS near Couette flow, which was formally obtained by Wasow in 1953.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.12029

Authors: Almog, Yaniv, Helffer, Bernard

Institutions: Braude College of Engineering Karmiel, Centre National de la Recherche Scientifique, Laboratoire de Mathématiques Jean Leray, Université de Nantes, Nantes Université

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7212733201

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