{"paper":{"title":"A global regularity result for the 2D Boussinesq equations with critical dissipation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Atanas Stefanov, Jiahong Wu","submitted_at":"2014-11-05T19:09:58Z","abstract_excerpt":"This paper examines the global regularity problem on the two-dimensional incompressible Boussinesq equations with fractional dissipation, given by $\\Lambda^\\alpha u$ in the velocity equation and by $\\Lambda^\\beta \\theta$ in the temperature equation, where $\\Lambda=\\sqrt{-\\Delta}$ denotes the Zygmund operator. We establish the global existence and smoothness of classical solutions when $(\\alpha,\\beta)$ is in the critical range: $\\alpha>\\frac{\\sqrt{1777}-23}{24} =0.798103..$, $\\beta>0$ and $\\alpha+ \\beta =1$. This result improves the previous work of Jiu, Miao, Wu and Zhang \\cite{JMWZ} which obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1362","kind":"arxiv","version":3},"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"}