A Hopf-Bifurcation Theorem for the Vorticity Formulation of the Navier–Stokes Equations in ℝ3

DOI10.1080/03605300802038536zbMath1153.37389OpenAlexW1979561485MaRDI QIDQ3518347

Hannes Uecker, Andreas Melcher, Guido Schneider

Publication date: 7 August 2008

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300802038536

zbMATH Keywords

periodic solutionsdecay ratesobstacle problem

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Stokes and related (Oseen, etc.) flows (76D07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Inequalities for trigonometric functions and polynomials (26D05) Stability and instability of nonparallel flows in hydrodynamic stability (76E09)

Related Items (8)

On bifurcating time-periodic flow of a Navier-Stokes liquid past a cylinder ⋮ Pacemakers in large arrays of oscillators with nonlocal coupling ⋮ The Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations ⋮ The existence of bifurcating invariant tori in a spatially extended reaction-diffusion-convection system with spatially localized amplification ⋮ Bifurcation of time-periodic solutions for the incompressible flow of nematic liquid crystals in three dimension ⋮ Deformation of striped patterns by inhomogeneities ⋮ Existence of periodic solutions of Boussinesq system ⋮ Inhomogeneities in 3 dimensional oscillatory media

Cites Work

• Unnamed Item
• Geometric theory of semilinear parabolic equations
• Hopf bifurcation and exchange of stability in diffusive media
• On the origination of auto-oscillations in flows
• Downstream asymptotics in exterior domains: from stationary wakes to time periodic flows
• On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems
• Mathematical questions relating to viscous fluid flow in an exterior domain
• Long-time asymptotics of the Navier-Stokes and vorticity equations on ℝ³
• Linear functional analysis. An application oriented introduction

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