Some 2.5D Models for the Primitive Equations of the Ocean and the Atmosphere

Qingshan Chen (1) , Jacques Laminie (2) , Antoine Rousseau (3) , Roger M. Temam (1, 2) , Joe Tribbia (4)

1 ISC - Institute for Scientific Computing and Applied Mathematics
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 MOISE - Modelling, Observations, Identification for Environmental Sciences
4 CGD - Climate and Global Dynamics Division [Boulder]

The primitive equations (PEs) of the atmosphere and the ocean without viscosity are considered. A 2.5D model is introduced, whose motivation is described in the Introduction. A set of nonlocal boundary conditions is proposed, and well-posedness is established for the flows linearized around a constant velocity stratified flow; homogeneous and nonhomogeneous boundary conditions are considered. A related model of dimension 2.5, of physical interest but with fewer degrees of freedom, is also considered at the end.

Mots clés: Nonviscous primitive equations; limited domains; boundary conditions; open boundary conditions; compatibility conditions; well-posedness; semigroup theory

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Dynamique des Fluides [physics.flu-dyn]; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]

Qingshan Chen, Jacques Laminie, Antoine Rousseau, Roger M. Temam, Joe Tribbia. Some 2.5D Models for the Primitive Equations of the Ocean and the Atmosphere. Analysis and Applications, 2007, 5 (3), pp.199-229. ⟨10.1142/S021953050700095X⟩. ⟨inria-00172578⟩