{"id":175,"date":"2023-11-07T13:16:55","date_gmt":"2023-11-07T04:16:55","guid":{"rendered":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/?page_id=175"},"modified":"2026-09-24T09:40:29","modified_gmt":"2026-09-24T00:40:29","slug":"seminar-fluidmath","status":"publish","type":"page","link":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/seminar-fluidmath\/","title":{"rendered":"\u6d41\u4f53\u6570\u5b66\u30bb\u30df\u30ca\u30fc"},"content":{"rendered":"<h2 align=\"center\">\u7b2c 29 \u56de\u3000\u6d41\u4f53\u6570\u5b66\u30bb\u30df\u30ca\u30fc<\/h2>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>\u65e5\u3000\u00a0 \u6642:\u00a0 2026 \u5e74 10 \u6708 8\u65e5(\u6728) 15\u664230\u5206 \uff5e 17\u6642<\/li>\n<li>\u5834\u6240\u30fb\u6559\u5ba4:\u3000\u304a\u8336\u306e\u6c34\u5973\u5b50\u5927\u5b66\u7406\u5b66\u90e8 1\u53f7\u9928 \u3000633\u6559\u5ba4<\/li>\n<li>\u8b1b \u6f14 \u8005:\u3000\u83f1\u7530 \u4fca\u660e \u6c0f(\u540d\u53e4\u5c4b\u5927\u5b66\u3000\u591a\u5143\u6570\u7406\u79d1\u5b66\u7814\u7a76\u79d1)<\/li>\n<li>\u8b1b\u6f14\u984c\u76ee:\u3000Large time decay of the fluid-structure semigroup subject to the \u00a0Navier slip-with-friction boundary condition<\/li>\n<li>\u8b1b\u6f14\u8981\u65e8:\u3000Consider the motion of a rigid body moving into a viscous incompressible fluid that fills the whole space in 3D. The fluid motion obeys the Navier-Stokes system, while the motion of the body is governed by the Newton law. Both motions are affected by each other at the fluid-solid interface through the Navier slip-with-friction boundary condition, which is known as a substitution for the no-slip one to resolve the no-collision paradox.<br \/>\nWe adopt a monolithic approach and carry out the spectral analysis to deduce the large time behavior of the fluid-structure semigroup, where the shape of the body is allowed to be arbitrary. What is remarkable is that the decay structure is somewhat different under the full slip condition when the body is axially symmetric. If, in particular, the body is a ball, we then apply the linear theory developed above to the nonlinear initial value problem to show the stability of the rest state. It is, furthermore, asymptotically stable except for the full slip case. This talk is based on a joint work with Bum Ja Jin (Mokpo, South Korea).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h2 align=\"center\">\u7b2c 30 \u56de\u3000\u6d41\u4f53\u6570\u5b66\u30bb\u30df\u30ca\u30fc<\/h2>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>\u65e5\u3000\u00a0 \u6642:\u00a0 2026 \u5e74 11 \u6708 19\u65e5(\u6728) 15\u664230\u5206 \uff5e 17\u6642<\/li>\n<li>\u5834\u6240\u30fb\u6559\u5ba4:\u3000\u304a\u8336\u306e\u6c34\u5973\u5b50\u5927\u5b66\u7406\u5b66\u90e8 1\u53f7\u9928 \u3000\u672a\u5b9a<\/li>\n<li>\u8b1b \u6f14 \u8005:\u3000\u9752\u6728\u3000\u57fa\u8a18 \u6c0f(\u6771\u4eac\u7406\u79d1\u5927\u5b66 \u5275\u57df\u7406\u5de5\u5b66\u90e8)<\/li>\n<li>\u8b1b\u6f14\u984c\u76ee:\u3000Onsager&#8217;s conjecture and energy conservation law for the Euler equation in bounded domains<\/li>\n<li>\u8b1b\u6f14\u8981\u65e8:\u3000In this talk, we consider sufficient conditions for weak solutions of the incompressible Euler equation in bounded domains to satisfy the energy conservation law.<br \/>\nThis problem is related to Onsager&#8217;s conjecture.\u3000Constantin&#8211;E&#8211;Titi proved energy conservation for weak solutions with regularity above 1\/3 in the whole space, and<br \/>\nCheskidov&#8211;Constantin&#8211;Friedlander&#8211;Shvydkoy established the corresponding result at the critical regularity 1\/3. For bounded domains, previous results corresponding to the result of<br \/>\nConstantin&#8211;E&#8211;Titi required an additional assumption near the boundary. We establish the energy conservation law in bounded domains under a condition corresponding to that of Cheskidov et al., using Besov spaces associated with the Stokes operator. Our approximation preserves the slip boundary condition, which allows us to remove the additional assumption near the boundary required in previous works. This is joint work with Tsukasa Iwabuchi (Tohoku University).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<p>\u3054\u8208\u5473\u304c\u3042\u308b\u65b9\u306f\u4e45\u4fdd\u307e\u3067\u3054\u9023\u7d61\u4e0b\u3055\u3044.<\/p>\n<p>\u307e\u305f,\u00a0 \u6d41\u4f53\u6570\u5b66\u30bb\u30df\u30ca\u30fc\u306f\u4eca\u5f8c\u4e0d\u5b9a\u671f\u3067\u958b\u50ac\u3059\u308b\u4e88\u5b9a\u3067\u3059.<\/p>\n<p>\u8b1b\u6f14\u8005\u304c\u6c7a\u307e\u308a\u307e\u3057\u305f\u3089,\u3053\u3053\u306b\u63b2\u793a\u3057\u307e\u3059.<\/p>\n<p>\u904e\u53bb\u306e\u30bb\u30df\u30ca\u30fc\u306e\u60c5\u5831\u306f\u3000<a href=\"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/seminar-fluidmath-info-old\/\">\u3053\u3061\u3089<\/a>\u3000\u3092\u3054\u89a7\u304f\u3060\u3055\u3044.<\/p>\n<p>\u6d41\u4f53\u6570\u5b66\u30bb\u30df\u30ca\u30fc\u3000\u4e16\u8a71\u4eba<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>\u9f4b\u85e4\u5e73\u548c(\u96fb\u6c17\u901a\u4fe1\u5927\u5b66)<\/li>\n<li>\u6751\u7530\u7f8e\u5e06(\u9759\u5ca1\u5927\u5b66)<\/li>\n<li>\u6e21\u908a\u572d\u5e02(\u516c\u7acb\u8acf\u8a2a\u6771\u4eac\u7406\u79d1\u5927\u5b66)<\/li>\n<li>\u4e45\u4fdd\u9686\u5fb9(\u304a\u8336\u306e\u6c34\u5973\u5b50\u5927\u5b66)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u7b2c 29 \u56de\u3000\u6d41\u4f53\u6570\u5b66\u30bb\u30df\u30ca\u30fc \u65e5\u3000\u00a0 \u6642:\u00a0 2026 \u5e74 10 \u6708 8\u65e5(\u6728) 15\u664230\u5206 \uff5e 17\u6642 \u5834\u6240\u30fb\u6559\u5ba4:\u3000\u304a\u8336\u306e\u6c34\u5973\u5b50\u5927\u5b66\u7406\u5b66\u90e8 1\u53f7\u9928 \u3000633\u6559\u5ba4 \u8b1b \u6f14 \u8005:\u3000\u83f1\u7530 \u4fca\u660e \u6c0f(\u540d\u53e4\u5c4b\u5927\u5b66\u3000\u591a\u5143\u6570\u7406 &hellip; <a href=\"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/seminar-fluidmath\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":51,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","vk-ltc-link":"","vk-ltc-target":"0"},"class_list":["post-175","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/pages\/175","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/users\/51"}],"replies":[{"embeddable":true,"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/comments?post=175"}],"version-history":[{"count":102,"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/pages\/175\/revisions"}],"predecessor-version":[{"id":408,"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/pages\/175\/revisions\/408"}],"wp:attachment":[{"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/media?parent=175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}