{"id":73966,"date":"2023-01-26T09:49:40","date_gmt":"2023-01-26T00:49:40","guid":{"rendered":"https:\/\/www.waseda.jp\/inst\/research\/?p=73966"},"modified":"2023-01-26T09:49:40","modified_gmt":"2023-01-26T00:49:40","slug":"stability-of-stationary-solutions-to-the-three-dimensional-navier-strokes-equations-with-surface-tension%ef%bc%88published-in-advances-in-nonlinear-analysis-january-2023%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.waseda.jp\/inst\/research\/news\/73966","title":{"rendered":"Stability of stationary solutions to the three-dimensional Navier-Strokes equations with surface tension\uff08Published in Advances in Nonlinear Analysis, January 2023\uff09"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n
Journal Title
\n\/\u63b2\u8f09\u30b8\u30e3\u30fc\u30ca\u30eb\u540d<\/td>\n		Advances in Nonlinear Analysis<\/td>\n<\/tr>\n
Publication Year and Month
\n\/\u63b2\u8f09\u5e74\u6708<\/td>\n		January, 2023<\/td>\n<\/tr>\n
Paper Title
\n\/\u8ad6\u6587\u30bf\u30a4\u30c8\u30eb<\/td>\n		Stability of stationary solutions to the three-dimensional Navier-Strokes equations with surface tension<\/td>\n<\/tr>\n
DOI
\n\/\u8ad6\u6587DOI<\/td>\n		10.1515\/anona-2022-0279<\/a><\/td>\n<\/tr>\n
\u00a0Author of Waseda University
\n\/\u672c\u5b66\u306e\u8457\u8005<\/td>\n		WATANABE, Keiichi(Assistant Professor(without tenure), Faculty of Science and Engineering, Global Center for Science and Engineering):First Author, Corresponding Author, Last Author<\/td>\n<\/tr>\n
Related Websites
\n\/\u95a2\u9023Web<\/td>\n		–<\/td>\n<\/tr>\n
Abstract
\n\/\u6284\u9332<\/td>\n		\n
\n

This article studies the stability of a stationary solution to the three-dimensional Navier-Stokes equations in a bounded domain, where surface tension effects are taken into account. More precisely, this article considers the stability of equilibrium figure of uniformly rotating viscous incompressible fluid in\u00a0R<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>\u00a0<\/span><\/span>, which are rotationally symmetric about a certain axis. It is proved that this stability result can be obtained by the positivity of the second variation of the energy functional associated with the equation that determines an equilibrium figure, provided that initial data are close to an equilibrium state. The unique global solution is constructed in the\u00a0L<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u00a0<\/span><\/span>-in-time and\u00a0L<\/span><\/span>q<\/span><\/span><\/span><\/span><\/span>\u00a0<\/span><\/span>-in-space setting with\u00a0(<\/span>p<\/span>,<\/span>q<\/span><\/span>)<\/span><\/span>\u2208<\/span>(<\/span>2<\/span>,<\/span>\u221e<\/span><\/span>)<\/span><\/span>\u00d7<\/span>(<\/span>3<\/span>,<\/span>\u221e<\/span><\/span>)<\/span><\/span><\/span><\/span>\u00a0<\/span><\/span>satisfying\u00a02<\/span><\/span>\/<\/span>p<\/span>+<\/span>3<\/span>\/<\/span><\/span>q<\/span><<\/span>1<\/span><\/span><\/span>\u00a0<\/span><\/span>, where the solution becomes real analytic, jointly in time and space. It is also proved that the solution converges exponentially to the equilibrium.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Journal Title \/\u63b2\u8f09\u30b8\u30e3\u30fc\u30ca\u30eb\u540d Advances in Nonlinear Analysis Publication Year and Month \/\u63b2\u8f09\u5e74\u6708 January, 2023 Paper Ti […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[],"tags":[218,217],"class_list":["post-73966","post","type-post","status-publish","format-standard","hentry","tag-impact-en","tag-impact"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.waseda.jp\/inst\/research\/wp-json\/wp\/v2\/posts\/73966","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.waseda.jp\/inst\/research\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.waseda.jp\/inst\/research\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/inst\/research\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/inst\/research\/wp-json\/wp\/v2\/comments?post=73966"}],"version-history":[{"count":1,"href":"https:\/\/www.waseda.jp\/inst\/research\/wp-json\/wp\/v2\/posts\/73966\/revisions"}],"predecessor-version":[{"id":73967,"href":"https:\/\/www.waseda.jp\/inst\/research\/wp-json\/wp\/v2\/posts\/73966\/revisions\/73967"}],"wp:attachment":[{"href":"https:\/\/www.waseda.jp\/inst\/research\/wp-json\/wp\/v2\/media?parent=73966"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.waseda.jp\/inst\/research\/wp-json\/wp\/v2\/categories?post=73966"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.waseda.jp\/inst\/research\/wp-json\/wp\/v2\/tags?post=73966"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}