{"paper":{"title":"Limits of the Stokes and Navier-Stokes equations in a punctured periodic domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriela Planas, James C. Robinson, Jerome Droniou, Michel Chipot, Wei Xue","submitted_at":"2014-07-25T15:32:24Z","abstract_excerpt":"In this paper we treat three problems on a two-dimensional `punctured periodic domain': we take $\\Omega_r=(-L,L)^2\\setminus D_r$, where $D_r=B(0,r)$ is the disc of radius $r$ centred at the origin. We impose periodic boundary conditions on the boundary of the box $\\Omega=(-L,L)^2$, and Dirichlet boundary conditions on the circumference of the disc. In this setting we consider the Poisson equation, the Stokes equations, and the time-dependent Navier-Stokes equations, all with a fixed forcing function $f$ (which must satisfy $\\int_\\Omega f=0$ for the stationary problems), and examine the behavio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6942","kind":"arxiv","version":2},"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"}