{"id":141,"date":"2015-04-03T13:47:27","date_gmt":"2015-04-03T20:47:27","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=141"},"modified":"2015-04-03T13:47:27","modified_gmt":"2015-04-03T20:47:27","slug":"vlad-vicol-aprin-6th","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2015\/04\/03\/vlad-vicol-aprin-6th\/","title":{"rendered":"Vlad Vicol (Aprin 6th)"},"content":{"rendered":"<p>\t\t\t\t&nbsp;<\/p>\n<p><strong>Speaker:<\/strong> Vlad Vicol (Princeton University)<\/p>\n<p><strong><span class=\"il\">Title<\/span>:<\/strong>&nbsp;Holder continuous solutions of active scalar equations<\/p>\n<div>\n<div><strong><span class=\"il\">Abstract<\/span>:&nbsp;<\/strong>We consider active scalar equations $\\partial_t \\theta + \\nabla \\cdot (u\\, \\theta) = 0$, where $u = T[\\theta]$ is a divergence-free velocity field, and $T$ is a Fourier multiplier operator. We prove that when $T$ is not an odd multiplier, there are nontrivial, compactly supported solutions weak solutions, with Holder regularity $C^{1\/9-}_{t,x}$. In fact, every integral conserving scalar field can be approximated in $D&#8217;$ by such solutions, and these weak solutions may be obtained from arbitrary initial data. We also show that when $T$ is odd, weak limits of solutions are solutions, so that the $h$-principle for odd active scalars may not be expected. This is a joint work with Phillip Isett (MIT).<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; Speaker: Vlad Vicol (Princeton University) Title:&nbsp;Holder continuous solutions of active scalar equations Abstract:&nbsp;We consider active scalar equations $\\partial_t \\theta + \\nabla \\cdot (u\\, \\theta) = 0$, where $u = T[\\theta]$ is a divergence-free velocity field, and $T$ is a Fourier multiplier operator. We prove that when $T$ is not an odd multiplier, there are [&hellip;]<\/p>\n","protected":false},"author":105,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-141","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/141","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\/105"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=141"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/141\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=141"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=141"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}