Analysis Seminar

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Well-Posedness of the Stokes-Coriolis System in the Half-Space Over a Rough Surface

Speaker: Anne-Laure Dalibard

Location: Warren Weaver Hall 1302

Date: Thursday, October 24, 2013, 11 a.m.

Synopsis:

This talk is devoted to the well-posedness of the 3d stationary Stokes-Coriolis system set in the half-space over a rough Lipschitz surface. The main issue lies in the fact that we work with solutions of infinite energy: indeed, the Dirichlet data for the Stokes-Coriolis system on the rough boundary does not decrease at infinity. Moreover, we do not assume any kind of spatial structure on the system, i.e. there is no underlying periodicity or stationarity. Following an idea of Gerard-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 horizontal 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 \(H^{1/2}_{uloc}\). This is a joint work with Christophe Prange.