{"paper":{"title":"Semi-group theory for the Stokes operator with Navier-type boundary conditions on $L^{p}$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ch\\'erif Amrouche, Hind Al Baba, Miguel Escobedo","submitted_at":"2016-01-22T14:37:42Z","abstract_excerpt":"In this article we consider the Stokes problem with Navier-type boundary conditions on a domain $\\Omega$, not necessarily simply connected. Since under these conditions the Stokes problem has a non trivial kernel, we also study the solutions lying in the orthogonal of that kernel. We prove the analyticity of several semigroups generated by the Stokes operator considered in different functional spaces. We obtain strong, weak and very weak solutions for the time dependent Stokes problem with the Navier-type boundary condition under different hypothesis on the initial data $\\boldsymbol{u}_0$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06019","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"}