{"paper":{"title":"Global Wellposedness for a Modified Critical Dissipative Quasi-Geostrophic Equation","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Changxing Miao, Liutang Xue","submitted_at":"2009-01-10T10:34:56Z","abstract_excerpt":"In this paper we consider the following modified quasi-geostrophic equation \n  \\partial_{t}\\theta+u\\cdot\\nabla\\theta+\\nu |D|^{\\alpha}\\theta=0,\n  \\quad u=|D|^{\\alpha-1}\\mathcal{R}^{\\bot}\\theta,\\quad x\\in\\mathbb{R}^2 with $\\nu>0$ and $\\alpha\\in ]0,1[\\,\\cup \\,]1,2[$. When $\\alpha\\in]0,1[$, the equation was firstly introduced by Constantin, Iyer and Wu in \\cite{ref ConstanIW}. Here, by using the modulus of continuity method, we prove the global well-posedness of the system with the smooth initial data. As a byproduct, we also show that for every $\\alpha\\in ]0,2[$, the Lipschitz norm of the solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1368","kind":"arxiv","version":6},"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"}