Subcritical bifurcations of shear flows
Analysis of PDEs
2026-03-09 v1
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 is small enough, provided the horizontal wave number 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.
Cite
@article{arxiv.2603.06322,
title = {Subcritical bifurcations of shear flows},
author = {Dongfen Bian and Shouyi Dai and Emmanuel Grenier},
journal= {arXiv preprint arXiv:2603.06322},
year = {2026}
}