Nonlinear boundary layers for rotating fluids

Anne-Laure Dalibard (1) , David Gérard-Varet (2, 3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 UPD7 - Université Paris Diderot - Paris 7
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We investigate the behavior of rotating incompressible flows near a non-flat horizontal bottom. In the flat case, the velocity profile is given explicitly by a simple linear ODE. When bottom variations are taken into account, it is governed by a nonlinear PDE system, with far less obvious mathematical properties. We establish the well-posedness of this system and the asymptotic behavior of the solution away from the boundary. In the course of the proof, we investigate in particular the action of pseudo-differential operators in non-localized Sobolev spaces. Our results extend the older paper [18], restricted to periodic variations of the bottom. It ponders on the recent linear analysis carried in [14].

Mots clés: rotating fluids; boundary layers; homogenization

Domaines: Equations aux dérivées partielles [math.AP]

Anne-Laure Dalibard, David Gérard-Varet. Nonlinear boundary layers for rotating fluids. Analysis & PDE, 2017. ⟨hal-01225236⟩