{"paper":{"title":"On the global regularity for the supercritical SQG equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michele Coti Zelati, Vlad Vicol","submitted_at":"2014-10-13T04:21:48Z","abstract_excerpt":"We consider the initial value problem for the fractionally dissipative quasi-geostrophic equation \\[ \\partial_t \\theta + \\mathcal{R}^\\perp \\theta \\cdot \\nabla \\theta + \\Lambda^\\gamma \\theta = 0, \\qquad \\theta(\\cdot,0) =\\theta_0 \\] on $\\mathbb{T}^2 = [0,1]^2$, with $\\gamma \\in (0,1)$. The coefficient in front of the dissipative term $\\Lambda^\\gamma = (-\\Delta)^{\\gamma/2}$ is normalized to $1$. We show that given a smooth initial datum with $\\|\\theta_0\\|_{L^2}^{\\gamma/2} \\|\\theta_0\\|_{\\dot{H}^2}^{1-\\gamma/2}\\leq R$, where {\\em $R$ is arbitrarily large}, there exists $\\gamma_1 = \\gamma_1(R) \\in ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3186","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"}