{"paper":{"title":"A Remark on the Global Well-posedness of a Modified Critical Quasi-geostrophic Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kazuo Yamazaki","submitted_at":"2010-06-01T21:04:13Z","abstract_excerpt":"The $\\beta$-generalized quasi-geostrophic equation is studied in the range of $\\alpha \\in (0, 1), \\beta \\in (1/2, 1), 1/2 < \\alpha + \\beta < 3/2$. When $\\alpha \\in (1/2, 1), \\beta \\in (1/2, 1)$ such that $1 \\leq \\alpha + \\beta < 3/2$, using the method introduced in [12] and [9], we prove global regularity of the unique and analytic solution and when $\\alpha \\in (0, 1/2), \\beta \\in (1/2, 1)$ such that $1/2 < \\alpha + \\beta < 1$, that there exists a constant such that $\\lVert \\nabla\\theta_{0}\\rVert_{L^{\\infty}}^{2-2\\alpha-2\\beta}\\lVert\\theta_{0}\\rVert_{L^{\\infty}}^{2\\alpha + 2\\beta - 1} \\leq c_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0253","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"}