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.

A Hopf Bifurcation in the Planar Navier-Stokes Equations

Gianni Arioli;
2021-01-01

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.
2021
Hopf bifurcation, Computer assisted proof, Periodic solutions, Navier-Stokes equation.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1176569
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