{"id":4424,"date":"2026-09-19T23:02:14","date_gmt":"2026-09-19T21:02:14","guid":{"rendered":"https:\/\/corot.top\/eva\/?p=4424"},"modified":"2026-09-19T23:02:14","modified_gmt":"2026-09-19T21:02:14","slug":"euler-ou-lagrange","status":"publish","type":"post","link":"https:\/\/corot.top\/eva\/?p=4424","title":{"rendered":"Euler ou Lagrange ?"},"content":{"rendered":"\n

Pour \u00e9tudier une rivi\u00e8re, on peut regarder l’eau couler depuis un pont (vision d’Euler) ou suivre une feuille \u00e0 la trace (vision de Lagrange).<\/p>\n\n\n\n

En r\u00e9solvant le probl\u00e8me du mill\u00e9naire de Navier-Stokes, l’IA a d\u00e9montr\u00e9 que le point de vue eul\u00e9rien seul n’est pas suffisant : les \u00e9quations finissent par \u00ab\u00a0crasher\u00a0\u00bb dans certains cas extr\u00eames (blow-up). R\u00e9sultat : on a toujours besoin de la m\u00e9thode lagrangienne pour prendre le relais et suivre les particules ! \u269b\ufe0f<\/p>\n\n\n\n

\ud83d\udcf8 En son honneur, voici une photo prise la semaine derni\u00e8re \u00e0 Turin : la seule statue de Lagrange, pr\u00e8s de sa maison natale, avec sa plaque un peu oubli\u00e9e. \ud83c\uddee\ud83c\uddf9\ud83d\udcf8 \ud83d\udc47
—
\u00abTo continue modeling the system, one would then need to track the behaviour of each particle individually [\u2026]
We follow the oscillations in particle coordinates, where their phase remains fixed. A particle starting at \u2018a\u2019 has trajectory X(t,a) given by \u2202\u209cX(t,a) = u(t, X(t,a)), X(0,a) = a.
We write a for a physical particle label [..] 
Let u be a smooth odd Euler velocity on \u211d\u00b3 \u00d7 [0, S], where 0 < S \u2264 1, with pressure p, and let X(t,a) be its particle map: X\u209c(t,a) = u(t, X(t,a)), X(0,a) = a.\u00bb
– Citation du papier public sur la r\u00e9solution de l’\u00e9quation d’Euler<\/p>\n\n\n\n

\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n<\/figure>\n","protected":false},"excerpt":{"rendered":"

Pour \u00e9tudier une rivi\u00e8re, on peut regarder l’eau couler depuis un pont (vision d’Euler) ou suivre une feuille \u00e0 la trace (vision de Lagrange). En r\u00e9solvant le probl\u00e8me du mill\u00e9naire de Navier-Stokes, l’IA a d\u00e9montr\u00e9 que le point de vue eul\u00e9rien seul n’est pas suffisant : les \u00e9quations finissent par \u00ab\u00a0crasher\u00a0\u00bb dans certains cas extr\u00eames […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[79],"tags":[158,57,51],"class_list":["post-4424","post","type-post","status-publish","format-standard","hentry","category-blog","tag-ia","tag-maths","tag-physique"],"_links":{"self":[{"href":"https:\/\/corot.top\/eva\/index.php?rest_route=\/wp\/v2\/posts\/4424","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/corot.top\/eva\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/corot.top\/eva\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/corot.top\/eva\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/corot.top\/eva\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4424"}],"version-history":[{"count":1,"href":"https:\/\/corot.top\/eva\/index.php?rest_route=\/wp\/v2\/posts\/4424\/revisions"}],"predecessor-version":[{"id":4427,"href":"https:\/\/corot.top\/eva\/index.php?rest_route=\/wp\/v2\/posts\/4424\/revisions\/4427"}],"wp:attachment":[{"href":"https:\/\/corot.top\/eva\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4424"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/corot.top\/eva\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4424"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/corot.top\/eva\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4424"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}