Boundary Driven Instabilities of Couette Flows

Dongfen Bian; Emmanuel Grenier; Nader Masmoudi; Weiren Zhao

doi:10.1007/s00220-025-05401-7

Boundary Driven Instabilities of Couette Flows

Dongfen Bian, Emmanuel Grenier^*, Nader Masmoudi, Weiren Zhao

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we prove that the threshold of instability of the classical Couette flow in Hs for large s is ν1/2. The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of width ν1/2 which is itself linearly unstable. This leads to a secondary instability which in turn creates a sub-layer.

Original language	English
Article number	221
Journal	Communications in Mathematical Physics
Volume	406
Issue number	9
DOIs	http://doi.org/10.1007/s00220-025-05401-7
Publication status	Published - Sept 2025

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title = "Boundary Driven Instabilities of Couette Flows",

abstract = "In this article, we prove that the threshold of instability of the classical Couette flow in Hs for large s is ν1/2. The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of width ν1/2 which is itself linearly unstable. This leads to a secondary instability which in turn creates a sub-layer.",

author = "Dongfen Bian and Emmanuel Grenier and Nader Masmoudi and Weiren Zhao",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.",

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AU - Bian, Dongfen

AU - Grenier, Emmanuel

AU - Masmoudi, Nader

AU - Zhao, Weiren

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

PY - 2025/9

Y1 - 2025/9

N2 - In this article, we prove that the threshold of instability of the classical Couette flow in Hs for large s is ν1/2. The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of width ν1/2 which is itself linearly unstable. This leads to a secondary instability which in turn creates a sub-layer.

AB - In this article, we prove that the threshold of instability of the classical Couette flow in Hs for large s is ν1/2. The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of width ν1/2 which is itself linearly unstable. This leads to a secondary instability which in turn creates a sub-layer.

UR - http://www.scopus.com/pages/publications/105012494494

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DO - 10.1007/s00220-025-05401-7

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SN - 0010-3616

VL - 406

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

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Boundary Driven Instabilities of Couette Flows

Abstract

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