A priori estimates for the 3D quasi-geostrophic system
Résumé
The present article is devoted to the study of the 3D dissipative quasi-geostrophic system (QG). This system can be obtained as limit model of the primitive equations in the asymptotics of strong rotation and stratification, and involves a non-radial, non-local, homogeneous pseudo-differential operator of order 2 denoted by Γ. After a refined study of the non-local part of Γ, we prove apriori estimates (in the general L p setting) for the 3D QG-model. The main difficulty of this article is to study the commutator of Γ with a Lagrangian change of variable.
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