{"paper":{"title":"Regularity of 3D axisymmetric Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daoyuan Fang, Hui Chen, Ting Zhang","submitted_at":"2015-05-05T07:38:20Z","abstract_excerpt":"In this paper, we study the three-dimensional axisymmetric Navier-Stokes system with nonzero swirl. By establishing a new key inequality for the pair $(\\frac{\\omega^{r}}{r},\\frac{\\omega^{\\theta}}{r})$, we get several Prodi-Serrin type regularity criteria based on the angular velocity, $u^\\theta$. Moreover, we obtain the global well-posedness result if the initial angular velocity $u_{0}^{\\theta}$ is appropriate small in the critical space $L^{3}(\\R^{3})$. Furthermore, we also get several Prodi-Serrin type regularity criteria based on one component of the solutions, say $\\omega^3$ or $u^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00905","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"}