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arXiv · 2009.12762

A Hopf bifurcation in the planar Navier-Stokes equations

Gianni Arioli·Hans Koch
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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.

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Gianni Arioli, Hans Koch. 2020-09-27. A Hopf bifurcation in the planar Navier-Stokes equations. https://doi.org/10.1007/s00021-021-00592-0

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