{"paper":{"title":"On the effect of external forces on incompressible fluid motions at large distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hyeong-Ohk Bae, Lorenzo Brandolese (ICJ)","submitted_at":"2014-02-23T20:13:16Z","abstract_excerpt":"We study incompressible Navier--Stokes flows in~$\\R^d$ with small and well localized data and external force~$f$. We establish pointwise estimates for large~$|x|$ of the form \\hbox{$c_t|x|^{-d}\\le |u(x,t)|\\le c'_t|x|^{-d}$}, where $c_t>0$ whenever $\\int_0^t\\!\\!\\int f(x,s)\\,dx\\,ds\\not=\\vec 0$. This sharply contrasts with the case of the Navier--Stokes equations without force, studied in [Brandolese, Vigneron, J. Math. Pures Appl. 88, 64--86 (2007)], where the spatial asymptotic behavior was $|u(x,t)|\\simeq C_t|x|^{-d-1}$. In particular, this shows that external forces with non-zero mean, no mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5663","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":""},"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"}