Bifurcation of symmetric domain walls for the Bénard-Rayleigh convection problem

Mariana Haragus (1) , Gérard Iooss (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 LJAD - Laboratoire Jean Alexandre Dieudonné

We prove the existence of domain walls for the Bénard-Rayleigh convection problem. Our approach relies upon a spatial dynamics formulation of the hydrodynamic problem, a center manifold reduction, and a normal form analysis of a reduced system. Domain walls are constructed as heteroclinic orbits of this reduced system.

Mots clés: Bénard-Rayleigh convection; bifurcations; domain walls; heteroclinic orbits; Normal forms of reversible systems

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]; Systèmes dynamiques [math.DS]; Formation de Structures et Solitons [nlin.PS]

Mariana Haragus, Gérard Iooss. Bifurcation of symmetric domain walls for the Bénard-Rayleigh convection problem. Archive for Rational Mechanics and Analysis, 2020. ⟨hal-02418271v1⟩