{"paper":{"title":"Global well-posedness for radial extremal hypersurface equation in $\\left(1+3 \\right)$-dimensional Minkowski space-time in critical Sobolev space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sheng Wang, Yi Zhou","submitted_at":"2022-12-17T09:40:45Z","abstract_excerpt":"In this article, we prove the global well-posedness in the critical Sobolev space $H_{rad}^2\\left(\\mathbb{R}^2\\right) \\times H_{rad}^1 \\left(\\mathbb{R}^2\\right)$ for the radial time-like extremal hypersurface equation in $\\left(1+3\\right)$- dimensional Minkowski space-time. This is achieved by deriving a new div-curl type lemma and combined it with energy and ``momentum\" balance law to get some space-time estimates of the nonlinearity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.08828","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/2212.08828/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"}