{"paper":{"title":"On the global well-posedness of a class of Boussinesq- Navier-Stokes systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Liutang Xue","submitted_at":"2009-10-02T02:37:43Z","abstract_excerpt":"In this paper we consider the following 2D Boussinesq-Navier-Stokes systems\n  \\partial_{t}u+u\\cdot\\nabla u+\\nabla p+ |D|^{\\alpha}u &= \\theta e_{2} \\partial_{t}\\theta+u\\cdot\\nabla \\theta+ |D|^{\\beta}\\theta &=0 \\quad with $\\textrm{div} u=0$ and $0<\\beta<\\alpha<1$. When $\\frac{6-\\sqrt{6}}{4}<\\alpha< 1$, $1-\\alpha<\\beta\\leq f(\\alpha) $, where $f(\\alpha)$ is an explicit function as a technical bound, we prove global well-posedness results for rough initial data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0311","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"}