{"id":3148,"date":"2026-08-07T16:08:45","date_gmt":"2026-08-07T15:08:45","guid":{"rendered":"https:\/\/andreabrussi.it\/a-pure-mathematical-version-of-the-clay-mathematics-institutes-navier-stokes-millennium-problem\/"},"modified":"2026-08-08T19:28:11","modified_gmt":"2026-08-08T18:28:11","slug":"a-pure-mathematical-version-of-the-clay-mathematics-institutes-navier-stokes-millennium-problem","status":"publish","type":"post","link":"https:\/\/andreabrussi.it\/it\/a-pure-mathematical-version-of-the-clay-mathematics-institutes-navier-stokes-millennium-problem\/","title":{"rendered":"A pure mathematical version of the Clay Mathematics Institute&#8217;s Navier-Stokes Millennium Problem"},"content":{"rendered":"<p>Abstract<br \/>\nThis report provides a rigorous transition from the physical formulation of the incompressible Navier-Stokes equations to their pure mathematical representation as defined by the Clay Mathematics Institute for the Millennium Prize Problems. We detail the physical meaning of each term in the classical equations and subsequently reformulate the problem strictly in the language of partial differential equations (PDEs) and operator theory, establishing the axiomatic constraints that govern the variables and parameters of the system.<\/p>\n<hr \/>\n<p><a href=\"https:\/\/andreabrussi.it\/wp-content\/uploads\/Brussi-2026_Navier-Stokes-Millennium-Problem.pdf\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-2140 size-full\" src=\"https:\/\/andreabrussi.it\/wp-content\/uploads\/pdf.png\" alt=\"pdf\" width=\"30\" height=\"30\" \/><\/a><a href=\"https:\/\/andreabrussi.it\/wp-content\/uploads\/Brussi-2026_Navier-Stokes-Millennium-Problem.pdf\" target=\"_blank\" rel=\"noopener\">Brussi 2026_Navier-Stokes Millennium Problem<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>Version uploaded to Zenodo: <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2568\" src=\"https:\/\/andreabrussi.it\/wp-content\/uploads\/link.png\" alt=\"link\" width=\"25\" height=\"30\" \/> <a href=\"https:\/\/doi.org\/10.5281\/zenodo.21852870\" target=\"_blank\" rel=\"noopener\"><strong>DOI &#8211; zenodo.21852870<\/strong><\/a><\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<p><a href=\"https:\/\/andreabrussi.it\/wp-content\/uploads\/Navier-Stokes-Millennium-Problem.png\" rel=\"lightbox[3148]\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-3145\" src=\"https:\/\/andreabrussi.it\/wp-content\/uploads\/Navier-Stokes-Millennium-Problem-300x103.png\" alt=\"Navier-Stokes Millennium Problem\" width=\"300\" height=\"103\" \/><\/a><\/p>\n<div style='text-align:right' class='yasr-auto-insert-visitor'><!--Yasr Visitor Votes Shortcode--><div id='yasr_visitor_votes_bcf76580086aa' class='yasr-visitor-votes'><div class=\"yasr-custom-text-vv-before yasr-custom-text-vv-before-3142\">please, rate this post<\/div><div id='yasr-vv-second-row-container-bcf76580086aa'\r\n                                        class='yasr-vv-second-row-container'><div id='yasr-visitor-votes-rater-bcf76580086aa'\r\n                                      class='yasr-rater-stars-vv'\r\n                                      data-rater-postid='3142'\r\n                                      data-rating='0'\r\n                                      data-rater-starsize='16'\r\n                                      data-rater-readonly='false'\r\n                                      data-rater-nonce='e5662b9442'\r\n                                      data-issingular='false'\r\n                                    ><\/div><div class=\"yasr-vv-stats-text-container\" id=\"yasr-vv-stats-text-container-bcf76580086aa\"><svg xmlns=\"https:\/\/www.w3.org\/2000\/svg\" width=\"20\" height=\"20\"\r\n                                   class=\"yasr-dashicons-visitor-stats\"\r\n                                   data-postid=\"3142\"\r\n                                   id=\"yasr-stats-dashicon-bcf76580086aa\">\r\n                                   <path d=\"M18 18v-16h-4v16h4zM12 18v-11h-4v11h4zM6 18v-8h-4v8h4z\"><\/path>\r\n                               <\/svg><span id=\"yasr-vv-text-container-bcf76580086aa\" class=\"yasr-vv-text-container\"><\/span><\/div><div id='yasr-vv-loader-bcf76580086aa' class='yasr-vv-container-loader'><\/div><\/div><div id='yasr-vv-bottom-container-bcf76580086aa'\r\n                              class='yasr-vv-bottom-container'\r\n                              style='display:none'><\/div><\/div><!--End Yasr Visitor Votes Shortcode--><\/div>","protected":false},"excerpt":{"rendered":"<p>Abstract This report provides a rigorous transition from the physical formulation of the incompressible Navier-Stokes equations to their pure mathematical representation as defined by the Clay Mathematics Institute for the Millennium Prize Problems. We detail the physical meaning of each term in the classical equations and subsequently reformulate the problem strictly in the language of &hellip; <a href=\"https:\/\/andreabrussi.it\/it\/a-pure-mathematical-version-of-the-clay-mathematics-institutes-navier-stokes-millennium-problem\/\" class=\"more-link\">Leggi tutto<span class=\"screen-reader-text\"> &#8220;A pure mathematical version of the Clay Mathematics Institute&#8217;s Navier-Stokes Millennium Problem&#8221;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"yasr_overall_rating":0,"yasr_post_is_review":"","yasr_auto_insert_disabled":"","yasr_review_type":"","footnotes":""},"categories":[56,57],"tags":[68,75,71],"class_list":["post-3148","post","type-post","status-publish","format-standard","hentry","category-fondamenti-della-fisica","category-matematica","tag-contributi-personali","tag-lavori","tag-recensioni"],"acf":[],"yasr_visitor_votes":{"stars_attributes":{"read_only":false,"span_bottom":false},"number_of_votes":0,"sum_votes":0},"_links":{"self":[{"href":"https:\/\/andreabrussi.it\/it\/wp-json\/wp\/v2\/posts\/3148","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/andreabrussi.it\/it\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/andreabrussi.it\/it\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/andreabrussi.it\/it\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/andreabrussi.it\/it\/wp-json\/wp\/v2\/comments?post=3148"}],"version-history":[{"count":3,"href":"https:\/\/andreabrussi.it\/it\/wp-json\/wp\/v2\/posts\/3148\/revisions"}],"predecessor-version":[{"id":3168,"href":"https:\/\/andreabrussi.it\/it\/wp-json\/wp\/v2\/posts\/3148\/revisions\/3168"}],"wp:attachment":[{"href":"https:\/\/andreabrussi.it\/it\/wp-json\/wp\/v2\/media?parent=3148"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/andreabrussi.it\/it\/wp-json\/wp\/v2\/categories?post=3148"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/andreabrussi.it\/it\/wp-json\/wp\/v2\/tags?post=3148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}