{"paper":{"title":"The global estimate for regular axially-symmetric solutions to the Navier Stokes equations coupled with the heat conduction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Wies{\\l}aw J. Grygierzec, Wojciech M. Zaj\\k{a}czkowski","submitted_at":"2025-01-30T12:24:31Z","abstract_excerpt":"The axially-symmetric solutions to the Navier-Stokes equations coupled with the heat conduction are considered. in a bounded cylinder $\\Omega \\subset \\mathbb{R}^3$. We assume that $v_r, v_{\\varphi}, \\omega_{\\varphi}$ vanish on the lateral part $S_1$ of the boundary $\\partial \\Omega$ and $v_z, \\omega_{\\varphi}, \\partial_z v_{\\varphi}$ vanish on the top and bottom of the cylinder, where we used standard cylindrical coordinates and $\\omega=\\text{rot} v$ is the vorticity of the fluid. Moreover, vanishing of the heat flux through the boundary is imposed. Assuming existence of a sufficiently regular"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18302","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/2501.18302/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"}