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arXiv · 1511.01856

Nonlinear boundary layers for rotating fluids

Anne-Laure Dalibard·David Gérard-Varet
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Abstract

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].

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Anne-Laure Dalibard, David Gérard-Varet. 2015-11-05. Nonlinear boundary layers for rotating fluids. https://arxiv.org/abs/1511.01856

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