{"paper":{"title":"Almost sure existence of Navier-Stokes Equations with randomized data in the whole space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cheng Yu, Dehua Wang, Robin Ming Chen, Song Yao","submitted_at":"2013-08-07T14:49:36Z","abstract_excerpt":"This paper considers the supercritical Navier-Stokes equations posed in the whole space $\\R^d$, with suitably randomized initial data, in the weak solution setting. The global weak solutions are constructed for a large set of initial data in $H^{-s}(\\R^d)$ for some $s>0$ via a probabilistic argument, and this in turn implies the almost sure existence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1588","kind":"arxiv","version":4},"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"}