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arXiv · 1707.07870

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

Frédéric Charve
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Abstract

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.

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Frédéric Charve. 2017-07-25. Global well-posedness and asymptotics for a penalized Boussinesq-type system without dispersion. https://arxiv.org/abs/1707.07870

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