{"paper":{"title":"$L^{2}-L^{\\infty}$ decay estimates and inviscid limits for Global smooth solutions to the compressible Navier-Stokes-Riesz system","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnieszka \\'Swierczewska-Gwiazda, Junhao Zhang, Yuan Xu","submitted_at":"2026-07-06T18:59:23Z","abstract_excerpt":"We study the Cauchy problem in $\\mathbb{R}^{3}$ for the repulsive compressible Navier-Stokes-Riesz system with Riesz exponent $0<s<1$ and viscosity $0<\\varepsilon\\leq1$, where the Riesz interaction $\\nabla(-\\Delta)^{-s}(\\rho-\\bar{\\rho})$ is a generalization of the Coulomb interaction for electrons. For small perturbations of a constant equilibrium, with the solenoidal component of the initial velocity of order $\\mathcal{O}(\\varepsilon)$, we prove the global existence and uniqueness of smooth solutions. We derive time-decay estimates in $L^{2}$ norms and $L^{\\infty}$ norms that capture both uni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05562","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/2607.05562/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"}