{"paper":{"title":"Analyticity for the (generalized) Navier-Stokes equations with rough initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baoxiang Wang, Chunyan Huang","submitted_at":"2013-10-08T14:09:50Z","abstract_excerpt":"We study the Cauchy problem for the (generalized) incompressible Navier-Stokes equations \\begin{align} u_t+(-\\Delta)^{\\alpha}u+u\\cdot \\nabla u +\\nabla p=0, \\ \\ {\\rm div} u=0, \\ \\ u(0,x)= u_0. \\nonumber \\end{align} We show the analyticity of the local solutions of the Navier-Stokes equation ($\\alpha=1$) with any initial data in critical Besov spaces $\\dot{B}^{n/p-1}_{p,q}(\\mathbb{R}^n)$ with $1< p<\\infty, \\ 1\\le q\\le \\infty $ and the solution is global if $u_0$ is sufficiently small in $\\dot{B}^{n/p-1}_{p,q}(\\mathbb{R}^n)$. In the case $p=\\infty$, the analyticity for the local solutions of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2141","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"}