{"paper":{"title":"Weak Solutions for Inviscid SQG with Lorentz Data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mihaela Ignatova, Peter Constantin, Quoc-Hung Nguyen","submitted_at":"2026-07-27T14:36:07Z","abstract_excerpt":"We construct global weak solutions of the inviscid surface quasi-geostrophic equation in $\\mathbb R^2$ and in smooth bounded domains, for arbitrary initial data in the critical Lorentz space $L^{4/3,2}$. The solutions conserve the Hamiltonian $\\|\\Lambda^{-1/2}\\theta(t)\\|_{L^2}^2$ for all times. The second Lorentz exponent is determined by the sharp boundedness $\\Lambda^{-1/2}:L^{4/3,2}\\to L^2$; the corresponding estimate fails for $L^{4/3,q}$ when $q>2$. We use an approximation scheme that is tailored for Lorentz spaces. It smooths the advecting velocity and the initial data, and preserves ord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24500","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24500/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"}