{"paper":{"title":"Global well-posedness for axisymmetric Boussinesq system with horizontal viscosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Changxing Miao, Xiaoxin Zheng","submitted_at":"2012-12-18T03:45:41Z","abstract_excerpt":"In this paper, we are concerned with the tridimensional anisotropic Boussinesq equations which can be described by {equation*}\n  {{array}{ll}\n  (\\partial_{t}+u\\cdot\\nabla)u-\\kappa\\Delta_{h} u+\\nabla \\Pi=\\rho e_{3},\\quad(t,x)\\in\\mathbb{R}^{+}\\times\\mathbb{R}^{3},\n  (\\partial_{t}+u\\cdot\\nabla)\\rho=0,\n  \\text{div}u=0.\n  {array}. {equation*} Under the assumption that the support of the axisymmetric initial data $\\rho_{0}(r,z)$ does not intersect the axis $(Oz)$, we prove the global well-posedness for this system with axisymmetric initial data. We first show the growth of the quantity $\\frac\\rho r$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4222","kind":"arxiv","version":2},"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"}