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Well-posedness of the
Stokes–Coriolis system in the half-space over a rough
surface
Anne-Laure Dalibard and Christophe Prange |
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Vol. 7 (2014), No. 6, 1253–1315
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Abstract |
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This paper is devoted to the well-posedness of the stationary D Stokes–Coriolis system set in a half-space with rough bottom and Dirichlet data which does not decrease at space infinity. Our system is a linearized version of the Ekman boundary layer system. We look for a solution of infinite energy in a space of Sobolev regularity. Following an idea of Gérard-Varet and Masmoudi, the general strategy is to reduce the problem to a bumpy channel bounded in the vertical direction thanks to a transparent boundary condition involving a Dirichlet to Neumann operator. Our analysis emphasizes some strong singularities of the Stokes–Coriolis operator at low tangential frequencies. One of the main features of our work lies in the definition of a Dirichlet to Neumann operator for the Stokes–Coriolis system with data in the Kato space . |
Keywords
Stokes–Coriolis system, Ekman boundary layer, rough
boundaries, Dirichlet to Neumann operator, Saint-Venant
estimate, Kato spaces
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Mathematical Subject Classification 2010
Primary: 35A22, 35C15, 35S99, 35A01
Secondary: 76U05, 35Q35, 35Q86
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Milestones
Received: 23 April 2013
Revised: 28 January 2014
Accepted: 1 March 2014
Published: 18 October 2014
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Authors |
| Anne-Laure Dalibard | |
| Université Pierre et Marie Curie
(Paris 6) UMR 7598 Laboratoire Jacques-Louis Lions F-75005 Paris France |
Centre national de la recherche
scientifique UMR 7598 Laboratoire Jacques-Louis Lions F-75005 Paris France |
| Christophe Prange | |
| Department of Mathematics The University of Chicago 5734 South University Avenue Chicago, 60637 United States |
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