Charve, Frédéric Global well-posedness and asymptotics for a penalized Boussinesq-type system without dispersion. (English) Zbl 1404.35447 Commun. Math. Sci. 16, No. 3, 791-807 (2018). Summary: J.-Y. Chemin proved the convergence (as the Rossby number \(\varepsilon\) goes to zero) of the solutions of the primitive equations to the solution of the 3D quasi-geostrophic system when the Froude number \(\mathrm F=1\) that is, when no dispersive property is available. The result was proved in the particular case where the kinematic viscosity \(\nu\) and the thermal diffusivity \(\nu^{\prime}\) 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. Cited in 4 Documents MSC: 35Q86 PDEs in connection with geophysics 35B45 A priori estimates in context of PDEs 35A01 Existence problems for PDEs: global existence, local existence, non-existence 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76U05 General theory of rotating fluids 76B65 Rossby waves (MSC2010) 86A05 Hydrology, hydrography, oceanography Keywords:geophysical fluids; primitive equations; Boussinesq system; 3D-quasi-geostrophic system PDFBibTeX XMLCite \textit{F. Charve}, Commun. Math. Sci. 16, No. 3, 791--807 (2018; Zbl 1404.35447) Full Text: DOI arXiv