{"paper":{"title":"Absence of local anomalous dissipation and local energy balance in 2D incompressible flows away from the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Helena J. Nussenzveig Lopes, Milton C. Lopes Filho, Tobias Barker","submitted_at":"2026-06-02T21:09:23Z","abstract_excerpt":"For the 2D Navier-Stokes equations with no-slip boundary condition, we consider the issue of whether anomalous dissipation away from the boundary vanishes. In particular, we show that such vanishing occurs if $u^{\\nu}$ is uniformily bounded in the Onsager supercritical space $L^{1+}_{t}L^{\\infty}_{x,loc}$ with appropriate bounds on the initial conditions. Our method involves arguments from \\cite{AD23} and \\cite{CW23} involving localization via modulation, together with vorticity energy type estimates inspired by \\cite{CFLS16} and estimates involving $L^2$-based structure functions inspired by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04218","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/2606.04218/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"}