{"paper":{"title":"Weak well-posedness by transport noise for a class of 2D fluid dynamics equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Dejun Luo, Lucio Galeati","submitted_at":"2023-05-15T16:20:15Z","abstract_excerpt":"A fundamental open problem in fluid dynamics is whether solutions to $2$D Euler equations with $(L^1_x\\cap L^p_x)$-valued vorticity are unique, for some $p\\in [1,\\infty)$. A related question, more probabilistic in flavour, is whether one can find a physically relevant noise regularizing the PDE. We present some substantial advances towards a resolution of the latter, by establishing well-posedness in law for solutions with $(L^1_x\\cap L^2_x)$-valued vorticity and finite kinetic energy, for a general class of stochastic 2D fluid dynamical equations; the noise is spatially rough and of Kraichnan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08761","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/2305.08761/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"}