{"paper":{"title":"Strong solutions to the 3D primitive equations with only horizontal dissipation: near $H^1$ initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.ao-ph","physics.flu-dyn","physics.geo-ph"],"primary_cat":"math.AP","authors_text":"Chongsheng Cao, Edriss S. Titi, Jinkai Li","submitted_at":"2016-07-21T10:09:35Z","abstract_excerpt":"In this paper, we consider the initial-boundary value problem of the three-dimensional primitive equations for oceanic and atmospheric dynamics with only horizontal viscosity and horizontal diffusivity. We establish the local, in time, well-posedness of strong solutions, for any initial data $(v_0, T_0)\\in H^1$, by using the local, in space, type energy estimate. We also establish the global well-posedness of strong solutions for this system, with any initial data $(v_0, T_0)\\in H^1\\cap L^\\infty$, such that $\\partial_zv_0\\in L^m$, for some $m\\in(2,\\infty)$, by using the logarithmic type anisot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06252","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"}