{"paper":{"title":"Analysis of a projection method for the Stokes problem using an $\\varepsilon$-Stokes approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adrian Muntean, Hirofumi Notsu, Kazunori Matsui, Masato Kimura","submitted_at":"2018-12-26T07:08:45Z","abstract_excerpt":"We generalize pressure boundary conditions of an $\\varepsilon$-Stokes problem. Our $\\varepsilon$-Stokes problem connects the classical Stokes problem and the corresponding pressure-Poisson equation using one parameter $\\varepsilon>0$. For the Dirichlet boundary condition, it is proven in K. Matsui and A. Muntean (2018) that the solution for the $\\varepsilon$-Stokes problem converges to the one for the Stokes problem as $\\varepsilon$ tends to 0, and to the one for the pressure-Poisson problem as $\\varepsilon$ tends to $\\infty$. Here, we extend these results to the Neumann and mixed boundary con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10250","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"}