{"paper":{"title":"On the Stokes system in cylindrical domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Joanna Renc{\\l}awowicz, Wojciech M. Zaj\\k{a}czkowski","submitted_at":"2021-11-15T21:07:59Z","abstract_excerpt":"The existence of solutions to some initial-boundary value problem for the Stokes system is proved. The result is shown in Sobolev-Slobodetskii spaces such that the velocity belongs to $W_r^{2+\\sigma,1+\\sigma/2}(\\Omega^T)$ and gradient of pressure to $W_r^{\\sigma,\\sigma/2}(\\Omega^T)$, where $r\\in(1,\\infty)$, $\\sigma\\in(0,1)$, $\\Omega^T=\\Omega\\times(0,T)$. These are special Besov spaces: $B_{r,r}^{2+\\sigma,1+\\sigma/2}(\\Omega^T)$ and $B_{r,r}^{\\sigma,\\sigma/2}(\\Omega^T)$, respectively. The existence is proved by the technique of regularizer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.08083","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/2111.08083/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"}