{"id":1073,"date":"2022-02-23T15:30:07","date_gmt":"2022-02-23T23:30:07","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=1073"},"modified":"2022-02-23T15:30:07","modified_gmt":"2022-02-23T23:30:07","slug":"sebastian-herr-bielefeld","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2022\/02\/23\/sebastian-herr-bielefeld\/","title":{"rendered":"Sebastian Herr (Bielefeld)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 2\/28, will be given by <em>Sebastian Herr<\/em> (Bielefeld University) online via Zoom from <strong>9:10am to 10:00am PST (NOTE THE SPECIAL TIME)<\/strong>. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu).<\/p>\n\n\n\n<p><strong>Title<\/strong>: Global wellposedness for the energy-critical Zakharov system below the ground state<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: The Zakharov system is a quadratically coupled system of a Schroedinger and a wave equation, which is related to the focussing cubic Schroedinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that it is globally well-posed in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr\\&#8221;odinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 2\/28, will be given by Sebastian Herr (Bielefeld University) online via Zoom from 9:10am to 10:00am PST (NOTE THE SPECIAL TIME). To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu). Title: Global wellposedness for the energy-critical Zakharov system below the ground state Abstract: The Zakharov system is a quadratically coupled system of a [&hellip;]<\/p>\n","protected":false},"author":106,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1073","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1073","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\/106"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1073"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1073\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1073"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1073"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1073"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}