A Hopf bifurcation in the planar Navier-Stokes equations

Abstract

We consider the Navier-Stokes equation for an incompressible viscous fluid on a square, satisfying Navier boundary conditions and being subjected to a time-independent force. As the kinematic viscosity is varied, a branch of stationary solutions is shown to undergo a Hopf bifurcation, where a periodic cycle branches from the stationary solution. Our proof is constructive and uses computer-assisted estimates.

16 pages, 1 figure

References in corpus (1)

• Spontaneous periodic orbits in the Navier-Stokes flow

Cited by in corpus (1)

• Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics