{"id":216681,"date":"2025-06-26T17:05:58","date_gmt":"2025-06-26T22:05:58","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2025\/06\/navier-stokes-existence-and-smoothness"},"modified":"2025-06-26T17:05:58","modified_gmt":"2025-06-26T22:05:58","slug":"navier-stokes-existence-and-smoothness","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2025\/06\/navier-stokes-existence-and-smoothness","title":{"rendered":"Navier\u2013Stokes existence and smoothness"},"content":{"rendered":"<p><\/p>\n<p><iframe style=\"display: block; margin: 0 auto; width: 100%; aspect-ratio: 4\/3; object-fit: contain;\" src=\"https:\/\/www.youtube.com\/embed\/XoefjJdFq6k?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope;\n   picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>The problem concerns the mathematical properties of solutions to the Navier\u2013Stokes equations, a system of partial differential equations that describe the motion of a fluid in space. Solutions to the Navier\u2013Stokes equations are used in many practical applications. However, theoretical understanding of the solutions to these equations is incomplete. In particular, solutions of the Navier\u2013Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The problem concerns the mathematical properties of solutions to the Navier\u2013Stokes equations, a system of partial differential equations that describe the motion of a fluid in space. Solutions to the Navier\u2013Stokes equations are used in many practical applications. However, theoretical understanding of the solutions to these equations is incomplete. In particular, solutions of the Navier\u2013Stokes [\u2026]<\/p>\n","protected":false},"author":709,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[38,41,2229,219,8],"tags":[],"class_list":["post-216681","post","type-post","status-publish","format-standard","hentry","category-engineering","category-information-science","category-mathematics","category-physics","category-space"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/216681","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/709"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=216681"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/216681\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=216681"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=216681"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=216681"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}