{"paper":{"title":"On decay properties of solutions to the Stokes equations with surface tension and gravity in the half space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hirokazu Saito, Yoshihiro Shibata","submitted_at":"2015-07-28T01:15:45Z","abstract_excerpt":"In this paper, we proved decay properties of solutions to the Stokes equations with surface tension and gravity in the half space $\\mathbf{R}_{+}^{N}=\\{(x',x_N)\\mid x'\\in\\mathbf{R}^{N-1},\\ x_N>0\\}$ $(N\\geq 2)$. In order to prove the decay properties, we first show that the zero points $\\lambda_\\pm$ of Lopatinskii determinant for some resolvent problem associated with the Stokes equations have the asymptotics: $\\lambda_\\pm=\\pm i c_g^{1/2}|\\xi'|^{1/2} -2|\\xi'|^2+O(|\\xi'|^{5/2})$ as $|\\xi'|\\to0$, where $c_g>0$ is the gravitational acceleration and $\\xi'\\in\\mathbf{R}^{N-1}$ is the tangential varia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07616","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"}