Bifurcations of Viscous Shear Flows in a Strip

TY - JOUR

T1 - Bifurcations of Viscous Shear Flows in a Strip

AU - Bian, D.

AU - Grenier, E.

AU - Haragus, M.

N1 - Publisher Copyright: © 2026 American Mathematical Society

PY - 2026/1

Y1 - 2026/1

N2 - It is well-established that shear flows in a periodic strip are linearly unstable for the incompressible Navier Stokes equations provided the viscosity is small enough. In this article, under a natural spectral assumption which is satisfied for convex or concave analytic flows, we prove that shear flows undergo a Hopf bifurcation near their upper marginal stability curve. In particular, near this curve, there exist solutions which are periodic in t and x.

AB - It is well-established that shear flows in a periodic strip are linearly unstable for the incompressible Navier Stokes equations provided the viscosity is small enough. In this article, under a natural spectral assumption which is satisfied for convex or concave analytic flows, we prove that shear flows undergo a Hopf bifurcation near their upper marginal stability curve. In particular, near this curve, there exist solutions which are periodic in t and x.

UR - https://www.scopus.com/pages/publications/105036295425

U2 - 10.1090/proc/17518

DO - 10.1090/proc/17518

M3 - Article

AN - SCOPUS:105036295425

SN - 0002-9939

VL - 154

SP - 1675

EP - 1684

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -