2025/01/04 by Bian Dongfen, Dongfen, Bian, Grenier Emmanuel +3
Engineering · Mathematics · #35B32 #35Q30 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.2501.02202
openalex publication_date 2025/01/04 · openalex created_date 2025/01/08 · openalex updated_date 2026/07/31
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.