{"paper":{"title":"Generic properties of the spectrum of the Stokes system with Dirichlet boundary condition in R^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Djalil Kateb, Ruixing Long, Yacine Chitour","submitted_at":"2013-03-18T18:50:49Z","abstract_excerpt":"Let (SD_\\Omega) be the Stokes operator defined in a bounded domain \\Omega of R^3 with Dirichlet boundary conditions. We prove that, generically with respect to the domain \\Omega with C^5 boundary, the spectrum of (SD_\\Omega) satisfies a non resonant property introduced by C. Foias and J. C. Saut to linearize the Navier-Stokes system in a bounded domain \\Omega of R^3 with Dirichlet boundary conditions. For that purpose, we first prove that, generically with respect to the domain \\Omega with C^5 boundary, all the eigenvalues of (SD_\\Omega) are simple. That answers positively a question raised by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4358","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"}