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Nonlinear boundary layers for rotating fluids

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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https://hal.archives-ouvertes.fr/hal-01225236
Contributor : Anne-Laure Dalibard <>
Submitted on : Thursday, November 5, 2015 - 6:17:11 PM
Last modification on : Wednesday, December 9, 2020 - 3:46:07 AM
Long-term archiving on: : Saturday, February 6, 2016 - 11:30:37 AM

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  • HAL Id : hal-01225236, version 1
  • ARXIV : 1511.01856

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

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