{"paper":{"title":"On the energy and helicity conservation of the incompressible Euler equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gnag Wu, Wei Wei, Yanqing Wang, Yulin Ye","submitted_at":"2023-07-17T08:39:46Z","abstract_excerpt":"In this paper, we are concerned with the minimal regularity of weak solutions implying the law of balance for both energy and helicity in the incompressible Euler equations. In the spirit of recent works due to Berselli [5] and Berselli-Georgiadis [6], it is shown that the energy of weak solutions is invariant if $v\\in L^{p}(0,T;B^{\\frac1p}_{\\frac{2p}{p-1},c(\\mathbb{N})} )$ with $1<p\\leq3$ and the helicity is conserved if $v\\in L^{p}(0,T;B^{\\frac2p}_{\\frac{2p}{p-1},c(\\mathbb{N})} )$ with $2<p\\leq3 $ for both the periodic domain and the whole space, which generalizes the classical work of Chesk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08322","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/2307.08322/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"}