{"id":1708,"date":"2024-09-29T01:27:45","date_gmt":"2024-09-29T01:27:45","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/apde\/?p=1708"},"modified":"2024-09-29T01:27:45","modified_gmt":"2024-09-29T01:27:45","slug":"koji-ohkitani-rims-kyoto-university","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2024\/09\/29\/koji-ohkitani-rims-kyoto-university\/","title":{"rendered":"Koji Ohkitani (RIMS, Kyoto University)"},"content":{"rendered":"<p>The APDE seminar on Monday, <span data-sheets-root=\"1\">9\/30<\/span>, will be given by <span data-sheets-root=\"1\">Koji Ohkitani (RIMS, Kyoto University)<\/span> in-person in <strong>Evans 740,<\/strong> and will also be broadcasted online via Zoom from <strong>4:10pm to 5:00pm PST<\/strong>. To participate, please email Federico Pasqualotto (<span id=\"eeb-707764-672440\">fpasqualotto@berkeley.edu<\/span>) or Mengxuan Yang (<span id=\"eeb-246247-12367\">mxyang@math.berkeley.edu<\/span>).<\/p>\n<p><strong>Title:<\/strong> Numerical determination of the self-similar profile<br \/>\nfor the 3D Navier-Stokes equations and its applications<\/p>\n<p><strong>Abstract:<\/strong> We present the forward self-similar profile for the 3D Navier-Stokes<br \/>\nequations, representing the late stage of decaying Navier-Stokes flows.<br \/>\nThe existence of such a profile has been known, but its precise functional<br \/>\nform has not been determined numerically, let alone mathematically.<\/p>\n<p>Here we determine the profile for the first time using numerical methods.<br \/>\nThis has been achieved by a combination of two things; a numerical method<br \/>\nof solving the Navier-Stokes equations in the whole space and the explicit<br \/>\nform of the linearised solution. Taking the initial data from the<br \/>\nlinearised solution, we solve the fully-nonlinear Navier-Stokes equations<br \/>\nto observe its convergence to a steady solution in the dynamically scaled<br \/>\nspace. We have confirmed that the nonlinear correction\u00a0 is small,<br \/>\nconsistent with the previous perturbative analysis. Applications of the<br \/>\nself-similar profile are briefly discussed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 9\/30, will be given by Koji Ohkitani (RIMS, Kyoto University) in-person in Evans 740, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu). Title: Numerical determination of the self-similar profile for the 3D Navier-Stokes equations [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1708","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1708","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/102"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1708"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1708\/revisions"}],"predecessor-version":[{"id":1709,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1708\/revisions\/1709"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1708"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1708"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1708"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}