Existence of orthogonal domain walls in Bénard-Rayleigh convection
Résumé
In Bénard-Rayleigh convection we consider the pattern defect in orthogonal domain walls connecting a set of convective rolls with another set of rolls orthogonal to the first set. This is understood as an heteroclinic orbit of a reversible system where the x-coordinate plays the role of time. This appears as a perturbation of the heteroclinic orbit proved to exist in a reduced 6-dimensional system studied by a variational method in [2], and analytically in [8]. We then prove the existence of a one parameter family of heteroclinic connections between orthogonal sets of rolls, which wave numbers (different in general) are linked with a shift of rolls parallel to the wall.
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