{"id":1296,"date":"2025-03-28T14:09:14","date_gmt":"2025-03-28T21:09:14","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1296"},"modified":"2025-05-04T19:35:33","modified_gmt":"2025-05-05T02:35:33","slug":"normal-forms-the-modified-energy-method-and-an-extension","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2025\/03\/28\/normal-forms-the-modified-energy-method-and-an-extension\/","title":{"rendered":"Normal Forms, the Modified Energy Method, and an Extension"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <strong>April 1st<\/strong>, will be at\u00a0<strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:<\/strong> Ryan Martinez<\/p>\n<p><strong>Abstract: <\/strong>The method of normal forms was introduced to PDEs by Shatah, who used it to<br \/>\nstudy the long time behavior of semilinear Klein Gordon equations and the method<br \/>\nhas been widely used in the context of semilinear problems. The modified energy<br \/>\nmethod of Hunter, Ifrim, Tataru, and Wong extends the idea of normal forms to<br \/>\nquasilinear problems.<\/p>\n<p>In this talk, we will discuss the method of normal forms, the related method<br \/>\nof modified energy, and my recent work which extends these in a novel way. The aim is<br \/>\nto give a selection of nonlinear PDEs which demonstrate in detail how these methods<br \/>\nare used, why they work, and what gains they achieve.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, April 1st, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker: Ryan Martinez Abstract: The method of normal forms was introduced to PDEs by Shatah, who used it to study the long time behavior of semilinear Klein Gordon equations and the method has been widely used in the context of semilinear problems. The modified [&hellip;]<\/p>\n","protected":false},"author":92,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[],"class_list":["post-1296","post","type-post","status-publish","format-standard","hentry","category-spring-2025"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1296","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/92"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1296"}],"version-history":[{"count":2,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1296\/revisions"}],"predecessor-version":[{"id":1299,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1296\/revisions\/1299"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1296"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1296"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1296"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}