Subcritical bifurcations of shear flows

Dongfen Bian; Shouyi Dai; Emmanuel Grenier

doi:10.1016/j.aml.2026.109965

Subcritical bifurcations of shear flows

Dongfen Bian
, Shouyi Dai
, Emmanuel Grenier^*

^*Corresponding author for this work

Beijing Institute of Technology
Chinese Academy of Sciences

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

Abstract

It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier–Stokes equations if the viscosity ν is small enough, provided the horizontal wave number α lies in a small interval, between the so called lower and upper marginal stability curves. Moreover, a Hopf bifurcation occurs at the upper marginal stability curve. In this article, for various shear flows, we give numerical evidences that this bifurcation is subcritical .

Original language	English
Article number	109965
Journal	Applied Mathematics Letters
Volume	179
DOIs	https://doi.org/10.1016/j.aml.2026.109965
Publication status	Published - Aug 2026
Externally published	Yes

Keywords

Hopf bifurcation
Navier Stokes equation
Shear flows
Stability

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10.1016/j.aml.2026.109965

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title = "Subcritical bifurcations of shear flows",

abstract = "It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier–Stokes equations if the viscosity ν is small enough, provided the horizontal wave number α lies in a small interval, between the so called lower and upper marginal stability curves. Moreover, a Hopf bifurcation occurs at the upper marginal stability curve. In this article, for various shear flows, we give numerical evidences that this bifurcation is subcritical .",

keywords = "Hopf bifurcation, Navier Stokes equation, Shear flows, Stability",

author = "Dongfen Bian and Shouyi Dai and Emmanuel Grenier",

note = "Publisher Copyright: {\textcopyright} 2026 Elsevier Ltd.",

year = "2026",

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doi = "10.1016/j.aml.2026.109965",

language = "English",

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AU - Bian, Dongfen

AU - Dai, Shouyi

AU - Grenier, Emmanuel

PY - 2026/8

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N2 - It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier–Stokes equations if the viscosity ν is small enough, provided the horizontal wave number α lies in a small interval, between the so called lower and upper marginal stability curves. Moreover, a Hopf bifurcation occurs at the upper marginal stability curve. In this article, for various shear flows, we give numerical evidences that this bifurcation is subcritical .

AB - It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier–Stokes equations if the viscosity ν is small enough, provided the horizontal wave number α lies in a small interval, between the so called lower and upper marginal stability curves. Moreover, a Hopf bifurcation occurs at the upper marginal stability curve. In this article, for various shear flows, we give numerical evidences that this bifurcation is subcritical .

KW - Hopf bifurcation

KW - Navier Stokes equation

KW - Shear flows

KW - Stability

UR - https://www.scopus.com/pages/publications/105034993390

U2 - 10.1016/j.aml.2026.109965

DO - 10.1016/j.aml.2026.109965

M3 - Article

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SN - 0893-9659

VL - 179

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 109965

ER -

Subcritical bifurcations of shear flows

Abstract

Keywords

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