Existence of bifurcating quasipatterns in steady Bénard-Rayleigh convection

DOI10.1007/s00205-018-1313-6zbMath1428.35032OpenAlexW2893469872MaRDI QIDQ1710991

Gérard Iooss, Boele L. J. Braaksma

Publication date: 24 January 2019

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-018-1313-6

zbMATH Keywords

rotational symmetrysmall divisor problemwave vectorNash-Moser processtruncated power series expansion

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Absolute and convective instability and stability in hydrodynamic stability (76E15) Nonlinear effects in hydrodynamic stability (76E30) Nonlinear elliptic equations (35J60) Second-order nonlinear hyperbolic equations (35L70) Navier-Stokes equations (35Q30) Convection in hydrodynamic stability (76E06) Bifurcations in context of PDEs (35B32)

Related Items

Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems, Spatially quasi-periodic solutions of the Euler equation, Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls, Bifurcation of symmetric domain walls for the Bénard-Rayleigh convection problem, Existence of quasipatterns in the superposition of two hexagonal patterns, Domain walls for the Bénard-Rayleigh convection problem with ``Rigid-free boundary conditions, Patterns and Quasipatterns from the Superposition of Two Hexagonal Lattices

Cites Work

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• Proof of quasipatterns for the Swift-Hohenberg equation
• An abstract Nash-Moser theorem with parameters and applications to PDEs
• Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions
• On the existence of quasipattern solutions of the Swift-Hohenberg equation
• Perturbation theory for linear operators.
• Convergence properties of the 8, 10 and 12 mode representations of quasipatterns
• Construction of periodic solutions of nonlinear wave equations in higher dimension
• Existence and nonuniqueness of rectangular solutions of the Benard problem
• Konvexität der Eigenkurven beim Benardschen Problem
• Stability and bifurcation in fluid dynamics
• Design of Parametrically Forced Patterns and Quasipatterns
• On the equations of steady-state convection
• Stability of convection flows