Small divisor problems in Fluid Mechanics. In memory of Klaus Kirchgässner

Gérard Iooss (1, 2)

1 IUF - Institut universitaire de France
2 LJAD - Laboratoire Jean Alexandre Dieudonné

Several small divisor problems occuring in Fluid Mechanics are presented. Two of them come from water waves: 3D periodic travelling gravity waves, and 2D standing gravity waves. The last example comes from quasipatterns observed for thin viscous horizontal fluid layers periodically vertically shaked (Faraday type experiment).

Mots clés: small divisors; water waves; quasipatterns

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

Gérard Iooss. Small divisor problems in Fluid Mechanics. In memory of Klaus Kirchgässner. Journal of Dynamics and Differential Equations, 2015, 27 (3), pp.14. ⟨10.1007/s10884-013-9317-2⟩. ⟨hal-01265177⟩