{"paper":{"title":"Martingale Suitable Weak Solutions of $3$-D Stochastic Navier-Stokes Equations with Vorticity Bounds","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Weiquan Chen, Zhao Dong","submitted_at":"2024-02-18T07:13:31Z","abstract_excerpt":"In this paper, we construct martingale suitable weak solutions for $3$-dimensional incompressible stochastic Navier-Stokes equations with generally non-linear noise. In deterministic setting, as widely known, ``suitable weak solutions'' are Leray-Hopf weak solutions enjoying two different types of local energy inequalities (LEIs). In stochastic setting, we apply the idea of ``martingale solution\", avoid transforming to random system, and show new stochastic versions of the two local energy inequalities. In particular, in additive and linear multiplicative noise case, OU-processes and the expon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.11482","kind":"arxiv","version":3},"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/2402.11482/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"}