{"paper":{"title":"On well-posedness of $\\alpha$-SQG equations in the half-plane","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"In-Jee Jeong, Junha Kim, Yao Yao","submitted_at":"2023-05-07T14:59:13Z","abstract_excerpt":"We investigate the well-posedness of $\\alpha$-SQG equations in the half-plane, where $\\alpha=0$ and $\\alpha=1$ correspond to the 2D Euler and SQG equations respectively. For $0<\\alpha \\le 1/2$, we prove local well-posedness in certain weighted anisotropic H\\\"older spaces. We also show that such a well-posedness result is sharp: for any $0<\\alpha \\le 1$, we prove nonexistence of H\\\"older regular solutions (with the H\\\"older regularity depending on $\\alpha$) for initial data smooth up to the boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.04300","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/2305.04300/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"}