{"paper":{"title":"On the axisymmetric Navier-Stokes flow passing a cone with the total-slip boundary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qi S. Zhang, Xin Yang, Zijin Li","submitted_at":"2026-05-24T15:35:34Z","abstract_excerpt":"For the incompressible Navier-Stokes flows passing a certain type of cones $D$ with the Navier total-slip boundary condition, we show that there exists an absolute constant $C_* > 0$ such that if\n  \\[\n  \\sup_{x\\in D}r|v_{0,\\theta}|\\leq C_* \\quad\\text{and}\\quad \\int_{D} r v_{0,\\theta}(x) \\mathrm{d} x = 0,\n  \\]\n  then there exists a unique global bounded strong solution with finite energy, where $r$ means the distance to the $z$ axis, and $v_{0,\\theta}$ represents the initial value of the azimuthal component of the velocity $\\boldsymbol{v}$. Unlike in the previous conclusion in \\cite{LPYZZZ24}, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25137","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25137/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}