Mathematical study of the equatorial Ekman boundary layer

  • Jean RaxEmail author


In this paper, we study the well-posedness of a simple model of boundary layer for rotating fluids between two concentric spheres near the equator. We show that this model can be seen as a degenerate elliptic equation, for which we prove an existence result thanks to a Lax–Milgram-type lemma. We also prove uniqueness under an additional integrability assumption and present a transparent boundary condition for such layers.


Boundary layer Degenerate elliptic system Ekman layer Geophysical fluids 

Mathematics Subject Classification

35J70 35Q86 76U05 



This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Program Grant Agreement No. 637653, project BLOC “Mathematical Study of Boundary Layers in Oceanic Motion.”


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis Lions, LJLLSorbonne Université, Université Paris-Diderot SPC, CNRSParisFrance

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