{"paper":{"title":"Almost optimal well-posedness for Chern--Simons gauged $O(3)$ sigma model under the Lorenz gauge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huali Zhang, Jie Zhou","submitted_at":"2026-07-18T12:07:24Z","abstract_excerpt":"In this paper, we study the low-regularity Cauchy problem for the Chern--Simons gauged $O(3)$ sigma model in $\\mathbb{R}^{1+d}$ ($d=1,2$) under the Lorenz gauge.\n  For $d=1$, we establish local well-posedness for initial data $(\\boldsymbol{\\phi}_0,\\mathbf{A}_0)\\in H^{s_1}(\\mathbb{R})\\times H^{s_1-1}(\\mathbb{R})$ with $s_1>\\frac12$. This improves the previous result of Jin and Huh \\cite{HJ} by one quarter of a derivative and is almost optimal in view of the scaling-invariant regularities $\\dot H^{1/2}(\\mathbb{R})$ for the matter field and $\\dot H^{-1/2}(\\mathbb{R})$ for the gauge field.\n  For $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16792","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/2607.16792/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"}