{"paper":{"title":"Local Well-Posedness for Vlasov--Poisson with $L^{d+}$ Initial Density and Fractional Velocity Regularity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Quoc-Hung Nguyen","submitted_at":"2026-07-27T13:18:24Z","abstract_excerpt":"We prove a local well-posedness criterion for the Vlasov--Poisson system on $\\R^d_x\\times\\R^d_v$, $d\\geq2$, under an anisotropic assumption on the initial distribution. The datum has finite mass, its weighted velocity supremum belongs to $L^p_x$ for some $p>d$, and it has an arbitrarily small positive H\\\"older regularity in the velocity variable, uniformly with respect to velocity and with the same spatial $L^p$ control. The main estimate is a nonlinear mixing bound \\[\n  [\\rho(t)]_{C^\\alpha_x}\\lesssim\n  t^{-d/p-\\epsilon}C(f_0),\n  \\qquad \\epsilon>0~~\\text{small}. \\] Thus the density is integrab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24400","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/2607.24400/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"}