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Article Dans Une Revue Analysis & PDE Année : 2014

Well-posedness of the Stokes-Coriolis system in the half-space over a rough surface

Résumé

This paper is devoted to the well-posedness of the stationary $3$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 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 $H^{1/2}_{uloc}$.
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Dates et versions

hal-00817359 , version 1 (24-04-2013)
hal-00817359 , version 2 (30-01-2014)

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Anne-Laure Dalibard, Christophe Prange. Well-posedness of the Stokes-Coriolis system in the half-space over a rough surface. Analysis & PDE, 2014, ⟨10.2140/apde.2014.7.1253⟩. ⟨hal-00817359v2⟩
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