Year: 2025
Type: preprint
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 $t$ and $x$.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7141152377
OpenAlex ID: W4406133437