{"paper":{"title":"Global well-posedness and asymptotics for a penalized Boussinesq-type system without dispersion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fr\\'ed\\'eric Charve (LAMA)","submitted_at":"2017-07-25T09:33:59Z","abstract_excerpt":"J.-Y. Chemin proved the convergence (as the Rossby number $\\epsilon$ 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 $\\nu$ and the thermal diffusivity $\\nu$ ' 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07870","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}