Global well-posedness and asymptotics for a penalized Boussinesq-type system without dispersion

Frédéric Charve (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

J.-Y. Chemin proved the convergence (as the Rossby number ε goes to zero) of the solutions of the Primitive Equations to the solution of the 3D quasi-geostrophic system when the Froude number F = 1 that is when no dispersive property is available. The result was proved in the particular case where the kinematic viscosity ν and the thermal diffusivity ν ′ are close. In this article we generalize this result for any choice of the viscosities, the key idea is to rely on a special feature of the quasi-geostrophic structure.

Mots clés: Primitive equations; Quasi-geostrophic model; A priori estimates

Domaines: Equations aux dérivées partielles [math.AP]

Frédéric Charve. Global well-posedness and asymptotics for a penalized Boussinesq-type system without dispersion. Communications in Mathematical Sciences, 2018, 16, pp.791-807. ⟨hal-01567310⟩