2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115503We show that in the limit of small Rossby number $\eps$, the primitive equations of the ocean (OPEs) can be approximated by ``higher-order quasi-geostrophic equations'' up to an exponential accuracy in $\eps$. This approximation assumes well-prepared initial data and is valid for a timescale of order one (independent of $\eps$). Our construction uses Gevrey regularity of the OPEs and a classical method to bound errors in higher-order perturbation theory.16 pagesAnalysis of PDEs35B25; 76U05text