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Nonlinear boundary
layers for rotating fluids
Anne-Laure Dalibard and David Gérard-Varet |
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Vol. 10 (2017), No. 1, 1–42
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Abstract |
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We investigate the behaviour of rotating incompressible flows near a nonflat 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 behaviour of the solution away from the boundary. In the course of the proof, we investigate in particular the action of pseudodifferential operators in nonlocalized Sobolev spaces. Our results extend an older paper of Gérard-Varet (J. Math. Pures Appl. 82:11 (2003), 1453–1498), restricted to periodic variations of the bottom, using the recent linear analysis of Dalibard and Prange (Anal. & PDE 7:6 (2014), 1253–1315). |
Keywords
fluid mechanics, geophysical fluids, Ekman layers, boundary
layers
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Mathematical Subject Classification 2010
Primary: 35Q30
Secondary: 35Q86
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Milestones
Received: 3 November 2015
Revised: 12 May 2016
Accepted: 13 October 2016
Published: 30 January 2017
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Authors |
| Anne-Laure Dalibard | |
| Sorbonne Universités UPMC Université Paris 06 CNRS, UMR 7598 Laboratoire Jacques-Louis Lions 4 place Jussieu 75005 Paris France |
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| David Gérard-Varet | |
| Université Paris Diderot Sorbonne Paris Cité Institut de Mathématiques de Jussieu-Paris Rive Gauche UMR 7586 F-75205 Paris France |
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