{"paper":{"title":"Compactly supported anomalous weak solutions for 2D Euler equations with vorticity in Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miriam Buck, Stefano Modena","submitted_at":"2024-05-29T15:56:36Z","abstract_excerpt":"In a previous work (arXiv:2306.05948), we constructed by convex integration examples of energy dissipating solutions to the 2D Euler equations on $\\mathbb{R}^2$ with vorticity in the real Hardy space $H^p(\\mathbb{R}^2)$. In the present paper, we develop tools that significantly improve that result in two ways: Firstly, we achieve vorticities in $H^p(\\mathbb{R}^2)$ in the optimal range $p\\in (0,1)$ compared to $(2/3,1)$ in our previous work. Secondly, the solutions constructed here possess compact support and in particular preserve linear and angular momenta."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19214","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/2405.19214/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"}