{"id":1809,"date":"2025-03-10T15:58:39","date_gmt":"2025-03-10T15:58:39","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/apde\/?p=1809"},"modified":"2025-03-10T15:58:39","modified_gmt":"2025-03-10T15:58:39","slug":"rana-badreddine-ucla","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2025\/03\/10\/rana-badreddine-ucla\/","title":{"rendered":"Rana Badreddine (UCLA)"},"content":{"rendered":"<p>The APDE seminar on Monday, <span data-sheets-root=\"1\">3\/17<\/span>, will be given by Rana Badreddine (UCLA) in-person in <strong>Evans 736,<\/strong> and will also be broadcasted online via Zoom from <strong>4:10pm to 5:00pm PST<\/strong>. To participate, please email Robert Schippa (<span id=\"eeb-322338-403021\">rschippa@berkeley.edu<\/span>).<\/p>\n<p><strong>Title: <\/strong>The Calogero-Moser derivative NLS equation<\/p>\n<p><strong>Abstract: <\/strong>We consider a type of nonlocal nonlinear derivative Schr\u00f6dinger equation on the torus, called the Calogero-Sutherland DNLS equation.We derive an explicit formula to the solution of this nonlinear PDE. Moreover, using the integrability tools, we establish the global well-posedness of this equation in all the Hardy-Sobolev spaces \\(H^s_+(\\mathbb{T}), s\\geq0\\) down to the critical regularity space, and under a mass assumption on the initial data for the focusing equation, and for arbitrary initial data for the defocusing equation. Finally, a sketch of the proof for extending the flow to the critical regularity \\(L^2_+(\\mathbb{T})\\) will be presented.<\/p>\n<div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 3\/17, will be given by Rana Badreddine (UCLA) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Robert Schippa (rschippa@berkeley.edu). Title: The Calogero-Moser derivative NLS equation Abstract: We consider a type of nonlocal nonlinear derivative Schr\u00f6dinger equation on [&hellip;]<\/p>\n","protected":false},"author":112,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1809","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1809","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/112"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1809"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1809\/revisions"}],"predecessor-version":[{"id":1810,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1809\/revisions\/1810"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1809"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1809"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}