Analysis & PDE

  • Anal. PDE
  • Volume 7, Number 6 (2014), 1253-1315.

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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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.

Article information

Anal. PDE, Volume 7, Number 6 (2014), 1253-1315.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35A22: Transform methods (e.g. integral transforms) 35C15: Integral representations of solutions 35S99: None of the above, but in this section 35A01: Existence problems: global existence, local existence, non-existence
Secondary: 76U05: Rotating fluids 35Q35: PDEs in connection with fluid mechanics 35Q86: PDEs in connection with geophysics

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


Dalibard, Anne-Laure; Prange, Christophe. Well-posedness of the Stokes–Coriolis system in the half-space over a rough surface. Anal. PDE 7 (2014), no. 6, 1253--1315. doi:10.2140/apde.2014.7.1253.

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