{"paper":{"title":"Well-posedness of the Viscous Boussinesq System in Besov Spaces of Negative Order Near Index $s=-1$","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Deng, Shangbin Cui","submitted_at":"2011-05-13T13:20:04Z","abstract_excerpt":"This paper is concerned with well-posedness of the Boussinesq system. We prove that the $n$ ($n\\ge2$) dimensional Boussinesq system is well-psoed for small initial data $(\\vec{u}_0,\\theta_0)$ ($\\nabla\\cdot\\vec{u}_0=0$) either in $({B}^{-1}_{\\infty,1}\\cap{B^{-1,1}_{\\infty,\\infty}})\\times{B}^{-1}_{p,r}$ or in ${B^{-1,1}_{\\infty,\\infty}}\\times{B}^{-1,\\epsilon}_{p,\\infty}$ if $r\\in[1,\\infty]$, $\\epsilon>0$ and $p\\in(\\frac{n}{2},\\infty)$, where $B^{s,\\epsilon}_{p,q}$ ($s\\in\\mathbb{R}$, $1\\leq p,q\\leq\\infty$, $\\epsilon>0$) is the logarithmically modified Besov space to the standard Besov space $B^{s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2722","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"}