{"id":562,"date":"2023-01-18T20:16:42","date_gmt":"2023-01-19T04:16:42","guid":{"rendered":"\/wp\/hades\/?p=562"},"modified":"2023-01-18T20:16:42","modified_gmt":"2023-01-19T04:16:42","slug":"almost-sure-scattering-below-scaling-regularity-for-the-nonlinear-schrodinger-equation-in-high-dimensions","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2023\/01\/18\/almost-sure-scattering-below-scaling-regularity-for-the-nonlinear-schrodinger-equation-in-high-dimensions\/","title":{"rendered":"Almost-sure scattering below scaling regularity for the nonlinear Schrodinger equation in high dimensions"},"content":{"rendered":"\n\t\t\t\t\n<p> The HADES seminar on Tuesday,\u00a0<strong>January 24th<\/strong>\u00a0will be at\u00a0<strong>3:30 pm<\/strong> in <strong>Room 740<\/strong>.<\/p>\n\n\n\n<p><strong>Speaker:<\/strong> Marsden Katie Sabrina Catherine Rosie<\/p>\n\n\n\n<p><strong>Abstract:<\/strong> In this talk we will discuss the Cauchy problem for the energy-critical nonlinear Schrodinger equation in high dimensions. It is well-known that this problem is well-posed for data in Sobolev spaces with regularity $s&gt;1$. The critical case $s=1$ was also shown to be globally well-posed with scattering by Ryckman-Vi\u015fan in the mid-2000s. In this talk we will show that even for some super-critical regularities, $s&lt;1$, the equation is \u201calmost-surely\u201d globally well-posed with respect to a certain randomisation of the initial data and exhibits scattering. <\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0January 24th\u00a0will be at\u00a03:30 pm in Room 740. Speaker: Marsden Katie Sabrina Catherine Rosie Abstract: In this talk we will discuss the Cauchy problem for the energy-critical nonlinear Schrodinger equation in high dimensions. It is well-known that this problem is well-posed for data in Sobolev spaces with regularity $s&gt;1$. The critical [&hellip;]<\/p>\n","protected":false},"author":88,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-562","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/562","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\/88"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=562"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/562\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=562"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=562"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=562"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}