Chinese Annals of Mathematics, Series B

, Volume 31, Issue 6, pp 939–952 | Cite as

Quasi-hydrostatic primitive equations for ocean global circulation models

  • Carine LucasEmail author
  • Madalina Petcu
  • Antoine Rousseau


Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the zero-limit of the aspect ratio, is more realistic than the classical hydrostatic model, since the traditional approximation that consists in neglecting a part of the Coriolis force is relaxed. After justifying the derivation of the model, the authors provide a rigorous proof of global existence of weak solutions, and well-posedness for strong solutions in dimension three.


Hydrostatic approximation Coriolis force Ocean global circulation models Primitive equations Traditional approximation 

2000 MR Subject Classification

76M45 76U05 35B40 35Q35 76M20 


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Copyright information

© Editorial Office of CAM (Fudan University) and Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Carine Lucas
    • 1
    Email author
  • Madalina Petcu
    • 2
  • Antoine Rousseau
    • 3
  1. 1.Laboratoire MAPMO (UMR 6628), Fédération Denis Poisson (FDP-FR2964)Université d’OrléansOrléans Cedex 2France
  2. 2.Laboratoire de Mathématiques et ApplicationsFuturoscope Chasseneuil CedexFrance
  3. 3.Laboratoire Jean KuntzmannINRIAGrenoble Cedex 9France

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