Subcritical bifurcations of shear flows

Dongfen Bian; Shouyi Dai; Emmanuel Grenier

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arXiv · 2603.06322

Subcritical bifurcations of shear flows

Dongfen Bian·Shouyi Dai·Emmanuel Grenier

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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 $\nu$ is small enough, provided the horizontal wave number $\alpha$ 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.

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Dongfen Bian, Shouyi Dai, Emmanuel Grenier. 2026-03-06. Subcritical bifurcations of shear flows. https://arxiv.org/abs/2603.06322

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