{"paper":{"title":"Remarks on well-posedness of the generalized surface quasi-geostrophic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huan Yu, Quansen Jiu, Xiaoxin Zheng","submitted_at":"2017-07-05T09:59:20Z","abstract_excerpt":"In this paper, we are concerned with the Cauchy problem of the generalized surface quasi-geostrophic (SQG) equation in which the velocity field is expressed as $u=K\\ast\\omega$, where $\\omega=\\omega(x,t)$ is an unknown function and $K(x)=\\frac{x^\\perp}{|x|^{2+2\\alpha}}, 0\\le\\alpha\\le \\frac12.$ When $\\alpha=0$, it is the two-dimensional Euler equations. When $\\alpha=\\frac 12$, it corresponds to the inviscid SQG. We will prove that if the existence interval of the smooth solution to the generalized SQG for some $0<\\alpha_0\\le\\frac12$ is $[0,T]$, then under the same initial data, the existence int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01290","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"}