{"paper":{"title":"Optimal decay for the compressible Navier-Stokes equations without additional smallness assumptions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiang Xu, Zhouping Xin","submitted_at":"2018-12-31T07:57:23Z","abstract_excerpt":"This work is concerned with the large time behavior of solutions to the barotropic compressible Navier-Stokes equations in $\\mathbb{R}^{d}(d\\geq2)$. Precisely, it is shown that if the initial density and velocity additionally belong to some Besov space $\\dot{B}^{-\\sigma_1}_{2,\\infty}$ with $\\sigma_1\\in (1-d/2, 2d/p-d/2]$, then the $L^p$ norm (the slightly stronger $\\dot{B}^{0}_{p,1}$ norm in fact) of global solutions admits the optimal decay $t^{-\\frac{d}{2}(\\frac 12-\\frac 1p)-\\frac{\\sigma_1}{2}}$ for $t\\rightarrow+\\infty$. In contrast to refined time-weighted approaches ([11,43]), a pure ener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11714","kind":"arxiv","version":2},"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/1812.11714/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"}