{"id":2830,"date":"2014-02-13T14:20:13","date_gmt":"2014-02-13T13:20:13","guid":{"rendered":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/?p=2830"},"modified":"2015-09-26T16:42:47","modified_gmt":"2015-09-26T14:42:47","slug":"progress-on-navier-stokes-regularity","status":"publish","type":"post","link":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/progress-on-navier-stokes-regularity\/","title":{"rendered":"Progress on Navier-Stokes regularity"},"content":{"rendered":"<p style=\"text-align: justify;\">To the very best of my knowledge, Kazakh professor\u00a0Mukhtarbay Otelbaev submitted a paper on the solution of the\u00a0<a href=\"http:\/\/en.wikipedia.org\/wiki\/Navier%E2%80%93Stokes_existence_and_smoothness\" target=\"_blank\">Navier-Stokes regularity<\/a>\u00a0Millenium problem. It seems that he had found an upper bound for a unique solution for the periodic boundary condition formulation of the problem. For the readers who are familiar with the notation, the main result is stated as follows.<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/navier.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-2831\" src=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/navier.png\" alt=\"navier\" width=\"819\" height=\"245\" srcset=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/navier.png 819w, https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/navier-300x89.png 300w, https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/navier-705x210.png 705w, https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/navier-450x134.png 450w\" sizes=\"auto, (max-width: 819px) 100vw, 819px\" \/><\/a><\/p>\n<p style=\"text-align: justify;\">This result is under review as we speak. In the end, we are hoping for a solution that is constructive, i.e. an algorithm that provides the solution itself, not only shows the existence of it &#8211; if so, this work might be an important stepping stone in this process. The translation of the main result without the proof is available <a href=\"https:\/\/github.com\/myw\/navier_stokes_translate\" target=\"_blank\">here<\/a>. <a href=\"http:\/\/terrytao.wordpress.com\/2014\/02\/04\/finite-time-blowup-for-an-averaged-three-dimensional-navier-stokes-equation\/\" target=\"_blank\">Terence Tao<\/a> also has some interesting recent results.<span style=\"font-size: 14px; line-height: 1.5em;\"><br \/>\n<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>To the very best of my knowledge, Kazakh professor\u00a0Mukhtarbay Otelbaev submitted a paper on the solution of the\u00a0Navier-Stokes regularity\u00a0Millenium problem. It seems that he had found an upper bound for a unique solution for the periodic boundary condition formulation of the problem. For the readers who are familiar with the notation, the main result is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2838,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[20],"tags":[68,67,204,69],"class_list":["post-2830","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news","tag-millenium-problem","tag-navier-stokes","tag-personal","tag-theoretical-mathematics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/fluid_icon2.png","jetpack_shortlink":"https:\/\/wp.me\/p8ZWyD-JE","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/posts\/2830","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/comments?post=2830"}],"version-history":[{"count":5,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/posts\/2830\/revisions"}],"predecessor-version":[{"id":3082,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/posts\/2830\/revisions\/3082"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/media\/2838"}],"wp:attachment":[{"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/media?parent=2830"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/categories?post=2830"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/tags?post=2830"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}