{"paper":{"title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bruno de Andrade","submitted_at":"2026-07-27T19:07:16Z","abstract_excerpt":"This manuscript investigates the Cauchy problem for an incompressible fluid flow governed by a dual-scale hereditary memory, representing a viscoelastic variant of the classical Navier-Stokes equations that captures anomalous momentum transport. The non-local dissipation breaks exact global scale invariance, dictating a pseudo-differential analysis within the H\\\"{o}rmander class $S^{-2}_{1,0}$ where the spatial gradient induces a fractional temporal penalty. We rigorously establish $L^q-L^p$ decay estimates and identify the critical Lebesgue threshold $p_c = N (\\frac{1+\\alpha_\\infty}{1-\\alpha_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25009","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/2607.25009/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"}