{"paper":{"title":"On the regularity of a class of generalized quasi-geostrophic equations","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Liutang Xue","submitted_at":"2010-11-29T12:32:33Z","abstract_excerpt":"In this article we consider the following generalized quasi-geostrophic equation\n  \\partial_t\\theta + u\\cdot\\nabla \\theta + \\nu \\Lambda^\\beta \\theta =0, \\quad u= \\Lambda^\\alpha \\mathcal{R}^\\bot\\theta, \\quad x\\in\\mathbb{R}^2, where $\\nu>0$, $\\Lambda:=\\sqrt{-\\Delta}$, $\\alpha\\in ]0,1[$ and $\\beta\\in ]0,2[$. We first show a general criterion yielding the nonlocal maximum principles for the whole space active scalars, then mainly by applying the general criterion, for the case $\\alpha\\in]0,1[$ and $\\beta\\in ]\\alpha+1,2]$ we obtain the global well-posedness of the system with smooth initial data; a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6214","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"}