{"paper":{"title":"Non-conservative $H^{\\frac 12-}$ weak solutions of the incompressible 3D Euler equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Matthew Novack, Nader Masmoudi, Tristan Buckmaster, Vlad Vicol","submitted_at":"2021-01-22T18:58:35Z","abstract_excerpt":"For any positive regularity parameter $\\beta < \\frac 12$, we construct non-conservative weak solutions of the 3D incompressible Euler equations which lie in $H^{\\beta}$ uniformly in time. In particular, we construct solutions which have an $L^2$-based regularity index \\emph{strictly larger} than $\\frac 13$, thus deviating from the $H^{\\frac{1}{3}}$-regularity corresponding to the Kolmogorov-Obhukov $\\frac 53$ power spectrum in the inertial range."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.09278","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/2101.09278/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"}