{"paper":{"title":"Minimal blow-up initial data in critical Fourier-Herz spaces for potential Navier-Stokes singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Jingyue Li, Xiaoxin Zheng","submitted_at":"2018-04-26T00:33:42Z","abstract_excerpt":"In this paper, we mainly prove the existence of the minimal blow-up initial data in critical Fourier-Herz space $F\\dot{B}^{2-{\\frac3p}}_{p,q}(\\RR^3)$ with $1<p\\leq\\infty$ and $1\\leq q<\\infty$ for the three dimensional incompressible potential Navier-Stokes equations by developing techniques of \"localization in space\" involving the partial regularity given by the De Giorgi iteration, weak-strong uniqueness, the short-time behaviour of the kinetic energy and stability of singularity of Calder\\'on's solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09842","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"}