{"id":396,"date":"2021-10-11T00:50:46","date_gmt":"2021-10-11T07:50:46","guid":{"rendered":"\/wp\/hades\/?p=396"},"modified":"2021-10-11T00:50:46","modified_gmt":"2021-10-11T07:50:46","slug":"well-posedness-for-the-dispersive-hunter-saxton-equation","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2021\/10\/11\/well-posedness-for-the-dispersive-hunter-saxton-equation\/","title":{"rendered":"Well-Posedness For The Dispersive Hunter-Saxton Equation"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday,&nbsp;<strong>October 12th<\/strong>,&nbsp;will be given by&nbsp;<strong>Ovidiu-Neculai Avadanei<\/strong> at&nbsp;<strong>5 pm<\/strong>&nbsp;in&nbsp;<strong>740 Evans<\/strong>.<\/p>\n\n\n\n<p><strong>Speaker<\/strong>: Ovidiu-Neculai Avadanei <\/p>\n\n\n\n<p><strong>Abstract<\/strong>: This talk represents a first step towards understanding the well-posedness for the dispersive Hunter-Saxton equation. This problem arises in the study of nematic liquid crystals, and its non-dispersive version is known to be completely integrable. Although the equation has formal similarities with the KdV equation, the lack of $L^2$ control gives it a quasilinear character, with only continuous dependence on initial data. Here, we prove the local and global well-posedness of the Cauchy problem using a normal form approach to construct modified energies, and frequency envelopes in order to prove the continuous dependence with respect to the initial data. This is joint work with Albert Ai.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,&nbsp;October 12th,&nbsp;will be given by&nbsp;Ovidiu-Neculai Avadanei at&nbsp;5 pm&nbsp;in&nbsp;740 Evans. Speaker: Ovidiu-Neculai Avadanei Abstract: This talk represents a first step towards understanding the well-posedness for the dispersive Hunter-Saxton equation. This problem arises in the study of nematic liquid crystals, and its non-dispersive version is known to be completely integrable. Although the equation [&hellip;]<\/p>\n","protected":false},"author":90,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-396","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/396","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\/90"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=396"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/396\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=396"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=396"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}