Nonlinear Stability of Bifurcating Front Solutions for the Taylor-Couette Problem

DOI<745::AID-ZAMM745>3.0.CO;2-9 10.1002/1521-4001(200011)80:11/12<745::AID-ZAMM745>3.0.CO;2-9zbMath0967.35109arXivnlin/0004027OpenAlexW2593219210MaRDI QIDQ4761309

Guido Schneider, Jean-Pierre Eckmann

Publication date: 25 April 2001

Full work available at URL: https://arxiv.org/abs/nlin/0004027

zbMATH Keywords

nonlinear stabilityTaylor vorticesflow of a viscous, incompressible fluid in the domain between two rotating cylidersmodulated front solutions

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) NLS equations (nonlinear Schrödinger equations) (35Q55) Hydrodynamic stability (76E99) Viscous vortex flows (76D17)

Related Items

Modulating traveling fronts in a dispersive Swift-Hohenberg equation coupled to an additional conservation law, Self-similar decay of spatially localized perturbations of the Nusselt solution for the inclined film problem, Modulating traveling fronts for the Swift-Hohenberg equation in the case of an additional conservation law, Almost global existence and transient self similar decay for Poiseuille flow at criticality for exponentially long times, Diffusive mixing of periodic wave trains in reaction-diffusion systems, Self-similar decay of localized perturbations in the integral boundary layer equation, Nonlinear stability of fast invading fronts in a Ginzburg–Landau equation with an additional conservation law

Cites Work

• Unnamed Item
• Unnamed Item
• Mathematical analysis of sideband instabilities with application to Rayleigh-Bénard convection
• Existence and non-existence of global solutions for a semilinear heat equation
• Propagating fronts and the center manifold theorem
• Solutions without phase-slip for the Ginsburg-Landau equation
• Renormalization group and the Ginzburg-Landau equation
• Weighted norms for the stability of traveling waves
• Multidimensional nonlinear diffusion arising in population genetics
• Nonlinear stability of Taylor vortices in infinite cylinders
• Bifurcating fronts for the Taylor-Couette problem in infinite cylinders
• Global existence results for pattern forming processes in infinite cylindrical domains -- applications to 3D Navier-Stokes problems
• The Ginzburg-Landau manifold is an attractor
• Stability of moving fronts in the Ginzburg-Landau equation
• A new estimate for the Ginzburg-Landau approximation on the real axis
• On the validity of the Ginzburg-Landau equation
• The nonlinear stability of front solutions for parabolic partial differential equations
• The Couette-Taylor problem
• Error estimates for the Ginzburg-Landau approximation
• Invariant manifolds for parabolic partial differential equations on unbounded domains
• The Eckhaus criterion for convection roll solutions of the Oberbeck-Boussinesq equations
• Geometric stability analysis for periodic solutions of the Swift-Hohenberg equation
• The time dependent amplitude equation for the Swift-Hohenberg problem
• Wave-solutions of reversible systems and applications
• Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation
• The validity of modulation equations for extended systems with cubic nonlinearities
• Local stability of critical fronts in nonlinear parabolic partial differential equations
• Attractors for modulation equations on unbounded domains-existence and comparison
• THE PRINCIPLE OF LINEARIZED INSTABILITY FOR SPACE-PERIODIC EQUILIBRIA OF NAVIER-STOKES ON AN INFINITE PLATE
• BRANCHING ANALYSIS FOR THE TAYLOR PROBLEM
• Finite bandwidth, finite amplitude convection
• Numerical simulation of incompressible flows within simple boundaries: accuracy