{"paper":{"title":"Forward self-similar solutions of the fractional Navier-Stokes Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baishun Lai, Changxing Miao, Xiaoxin Zheng","submitted_at":"2017-10-22T23:51:04Z","abstract_excerpt":"We study forward self-similar solutions to the 3-D Navier-Stokes equations with the fractional diffusion $(-\\Delta)^{\\alpha}.$ First, we construct a global-time forward self-similar solutions to the fractional Navier-Stokes equations with $5/6<\\alpha\\leq1$ for arbitrarily large self-similar initial data by making use of the so called blow-up argument. Moreover, we prove that this solution is smooth in $\\mathbb R^3\\times (0,+\\infty)$. In particular, when $\\alpha=1$, we prove that the solution constructed by Korobkov-Tsai [Anal. PDE 9 (2016), 1811-1827] satisfies the decay estimate by establishi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08041","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":""},"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"}