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2014 Well-posedness of the Stokes–Coriolis system in the half-space over a rough surface
Anne-Laure Dalibard, Christophe Prange
Anal. PDE 7(6): 1253-1315 (2014). DOI: 10.2140/apde.2014.7.1253

Abstract

This paper is devoted to the well-posedness of the stationary 3D 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 Huloc12.

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Anne-Laure Dalibard. Christophe Prange. "Well-posedness of the Stokes–Coriolis system in the half-space over a rough surface." Anal. PDE 7 (6) 1253 - 1315, 2014. https://doi.org/10.2140/apde.2014.7.1253

Information

Received: 23 April 2013; Revised: 28 January 2014; Accepted: 1 March 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1304.35535
MathSciNet: MR3270164
Digital Object Identifier: 10.2140/apde.2014.7.1253

Subjects:
Primary: 35A01 , 35A22 , 35C15 , 35S99
Secondary: 35Q35 , 35Q86 , 76U05

Keywords: Dirichlet to Neumann operator , Ekman boundary layer , Kato spaces , rough boundaries , Saint-Venant estimate , Stokes–Coriolis system

Rights: Copyright © 2014 Mathematical Sciences Publishers

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