{"paper":{"title":"Strong ill-posedness and non-existence in Sobolev spaces for generalized-SQG","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego C\\'ordoba, Jos\\'e Lucas-Manch\\'on, Luis Mart\\'inez-Zoroa","submitted_at":"2025-02-10T11:17:56Z","abstract_excerpt":"The general surface quasi-geostrophic equation is the scalar transport equation defined by \\begin{equation*}\n  \\frac{\\partial \\theta}{\\partial t}+v^\\gamma_1 \\frac{\\partial \\theta}{\\partial x_1}+v^\\gamma_2 \\frac{\\partial \\theta}{\\partial x_2} =0 ,\n  \\end{equation*} where the velocity comes defined by\n  \\begin{equation*}\n  v^\\gamma=\\nabla^{\\perp} \\psi_\\gamma=\\left(\\partial_{2} \\psi_\\gamma,-\\partial_{1} \\psi_\\gamma \\right), \\quad \\psi_\\gamma=-\\Lambda^{-1+\\gamma} \\theta,\n  \\end{equation*} and $\\theta(\\cdot,0)=\\theta_0(\\cdot)$ is the initial condition. We consider the parameter $\\gamma \\in (-1,1)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06357","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.06357/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}