{"id":888,"date":"2024-04-13T21:38:12","date_gmt":"2024-04-14T04:38:12","guid":{"rendered":"\/wp\/hades\/?p=888"},"modified":"2024-04-13T21:38:12","modified_gmt":"2024-04-14T04:38:12","slug":"two-dimensional-gravity-water-waves-with-constant-vorticity-at-low-regularity","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2024\/04\/13\/two-dimensional-gravity-water-waves-with-constant-vorticity-at-low-regularity\/","title":{"rendered":"Two dimensional gravity water waves with constant vorticity at low regularity"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday,&nbsp;<strong>April 16th<\/strong>, will be at <strong>3:30pm<\/strong>&nbsp;in&nbsp;<strong>Room 939.<\/strong><\/p>\n\n\n\n<p><strong>Speaker<\/strong>: Lizhe Wan, University of Wisconsin-Madison<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: In this talk I will discuss the Cauchy problem of two-dimensional gravity water waves with constant vorticity. The water waves system is a nonlinear dispersive system that characterizes the evolution of free boundary fluid flows. I will describe the balanced energy estimates by Ai-Ifrim-Tataru and show that using this method, the water waves system is locally well-posed in $H^{\\frac{3}{4}}\\times H^{\\frac{5}{4}}$. This is a low regularity well-posedness result that effectively lowers $\\frac{1}{4}$ Sobolev regularity compared to the previous result.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,&nbsp;April 16th, will be at 3:30pm&nbsp;in&nbsp;Room 939. Speaker: Lizhe Wan, University of Wisconsin-Madison Abstract: In this talk I will discuss the Cauchy problem of two-dimensional gravity water waves with constant vorticity. The water waves system is a nonlinear dispersive system that characterizes the evolution of free boundary fluid flows. I will [&hellip;]<\/p>\n","protected":false},"author":94,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-888","post","type-post","status-publish","format-standard","hentry","category-spring-2024"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/888","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\/94"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=888"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/888\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=888"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=888"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=888"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}