Gianni Arioli, Hans Koch
A Hopf bifurcation in the planar Navier-Stokes equations
(539K, pdf)
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.