{"paper":{"title":"On the $\\mathcal{R}$-boundedness of solution operator families for two-phase Stokes resolvent equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hirokazu Saito, Sri Maryani","submitted_at":"2016-06-28T09:34:50Z","abstract_excerpt":"The aim of this paper is to show the existence of $\\mathcal{R}$-bounded solution operator families for two-phase Stokes resolvent equations in $\\dot\\Omega=\\Omega_+\\cup\\Omega_-$, where $\\Omega_\\pm$ are uniform $W_r^{2-1/r}$ domains of $N$-dimensional Euclidean space $\\mathbf{R}^N$ ($N\\geq 2$, $N<r<\\infty$). More precisely, given a uniform $W_r^{2-1/r}$ domain $\\Omega$ with two boundaries $\\Gamma_\\pm$ satisfying $\\Gamma_+\\cap\\Gamma_-=\\emptyset$, we suppose that some hypersurface $\\Gamma$ divides $\\Omega$ into two sub-domains, that is, there exist domains $\\Omega_\\pm\\subset\\Omega$ such that $\\Ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08625","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"}