Bifurcations of viscous shear flows in a strip
Abstract
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 t and x x .
Fields of Study & Subjects
Navier-Stokes equation solutions
Fluid Dynamics and Turbulent Flows
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 4
- Pages
- 1675–1684
- Publication date
- 10 February 2026
- Language
- EN