{"id":52,"date":"2021-12-06T15:47:55","date_gmt":"2021-12-06T18:47:55","guid":{"rendered":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/?p=52"},"modified":"2022-04-13T22:43:47","modified_gmt":"2022-04-14T02:43:47","slug":"maximal-function-estimates-and-local-well-posedness-for-the-generalized-zakharov-kuznetsov-equation","status":"publish","type":"post","link":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/2021\/12\/maximal-function-estimates-and-local-well-posedness-for-the-generalized-zakharov-kuznetsov-equation\/","title":{"rendered":"Maximal function estimates and local well-posedness for the generalized Zakharov\u2013Kuznetsov equation"},"content":{"rendered":"<h3>Speaker: <a href=\"https:\/\/w3.impa.br\/~linares\/\" target=\"_blank\" rel=\"noopener\">Felipe Linares<\/a><br \/>\nIMPA, Brazil<\/h3>\n<h3>Date: December 9, 2021 at 16:15 Santiago time<\/h3>\n<p><strong>Abstract:<\/strong> In this talk we will discuss recent results regarding local well-posedness for the generalized Zakharov\u2013Kuznetsov equation. We prove a high-dimensional version of the Strichartz estimates for the unitary group associated with the free Zakharov-Kuznetsov equation. As a by-product, we deduce maximal estimates which allow us to prove local well-posedness for the generalized Zakharov-Kuznetsov equation in the whole subcritical case whenever d\\ge 4, k\\ge 4 complementing the recent results of Kinoshita and Herr-Kinoshita. Finally, we use some of those maximal estimates in order to prove pointwise convergence results for the flow of the generalized Zakharov\u2013Kuznetsov equation in any dimension, in the same spirit of a recent manuscript by Compaan, Luc\u00e0 and Staffilani.<\/p>\n<p><strong>Venue:<\/strong> Online via Zoom \/ Sala de seminarios DIM, Beauchef 851, piso 5<br \/>\n<strong>Chair:<\/strong> Claudio Mu\u00f1oz<\/p>\n<a href=\"https:\/\/youtu.be\/UyfuV4GQQpw\" class=\"su-button su-button-style-flat\" style=\"color:#FFFFFF;background-color:#bc360a;border-color:#972c08;border-radius:7px\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"color:#FFFFFF;padding:7px 20px;font-size:16px;line-height:24px;border-color:#d17354;border-radius:7px;text-shadow:none\"><i class=\"sui sui-youtube-play\" style=\"font-size:16px;color:#FFFFFF\"><\/i> YouTube video (in English)<\/span><\/a>\n<p>&nbsp;<\/p>\n<div class=\"su-youtube su-u-responsive-media-yes\"><iframe loading=\"lazy\" width=\"600\" height=\"400\" src=\"https:\/\/www.youtube.com\/embed\/UyfuV4GQQpw?\" frameborder=\"0\" allowfullscreen allow=\"autoplay; encrypted-media; picture-in-picture\" title=\"\"><\/iframe><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Felipe Linares (IMPA, Brazil)<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[5],"tags":[],"class_list":["post-52","post","type-post","status-publish","format-standard","hentry","category-past-seminar"],"_links":{"self":[{"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts\/52","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/comments?post=52"}],"version-history":[{"count":10,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts\/52\/revisions"}],"predecessor-version":[{"id":170,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts\/52\/revisions\/170"}],"wp:attachment":[{"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/media?parent=52"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/categories?post=52"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/tags?post=52"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}