Quasi-hydrostatic primitive equations for ocean global circulation models

Abstract : 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, we provide a rigorous proof of global existence of weak solutions, and well-posedness for strong solutions in dimension three.
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Carine Lucas, Madalina Petcu, Antoine Rousseau. Quasi-hydrostatic primitive equations for ocean global circulation models. Chinese Annals of Mathematics - Series B, Springer Verlag, 2010, 31 (6), pp.939-952. 〈10.1007/s11401-010-0611-6〉. 〈hal-00544799〉

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