{"paper":{"title":"A sparse resolution of the DiPerna-Majda gap problem for $2$D Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Daniel Spector, Oscar Dom\\'inguez","submitted_at":"2024-09-04T00:12:49Z","abstract_excerpt":"A central question which originates in the celebrated work in the 1980's of DiPerna and Majda asks what is the optimal decay $f > 0$ such that uniform rates $|\\omega|(Q) \\leq f(|Q|)$ of the vorticity maximal functions guarantee strong convergence without concentrations of approximate solutions to energy-conserving weak solutions of the $2$D Euler equations with vortex sheet initial data. A famous result of Majda (1993) shows $f(r) = [\\log (1/r)]^{-1/2}$, $r<1/2$, as the optimal decay for \\emph{distinguished} sign vortex sheets. In the general setting of \\emph{mixed} sign vortex sheets, DiPerna"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.02344","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/2409.02344/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"}