{"id":751,"date":"2023-10-24T07:29:27","date_gmt":"2023-10-24T14:29:27","guid":{"rendered":"\/wp\/hades\/?p=751"},"modified":"2023-10-24T07:29:27","modified_gmt":"2023-10-24T14:29:27","slug":"optimal-enhanced-dissipation-for-geodesic-flows","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2023\/10\/24\/optimal-enhanced-dissipation-for-geodesic-flows\/","title":{"rendered":"Optimal enhanced dissipation for geodesic flows"},"content":{"rendered":"\n\t\t\t\t\n<p class=\"wp-block-paragraph\">The HADES seminar on Tuesday, <strong>October 31st<\/strong>&nbsp;will be at&nbsp;<strong>3:30pm<\/strong>&nbsp;in&nbsp;<strong>Room 740<\/strong>. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Speaker: <\/strong><a href=\"https:\/\/math.berkeley.edu\/~zworski\/\">Maciej Zworski<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract: <\/strong> We consider geodesic flows on negatively curved compact manifolds or more generally contact Anosov flows (all these concepts will be pedagogically explained). The object is to show that if $ X $ is the generator of the flow and $ \\Delta $, a (negative) Laplacian, then solutions to the convection diffusion equation, $ \\partial_t u = X u +\u00a0 \\nu \\Delta $, $ \\nu \\geq 0 $,\u00a0 satisfy \\[\u00a0 \u00a0 \\| u ( t )\u00a0 \u00a0&#8211;\u00a0 \\underline u \\|_{L^2 ( M) } \\leq C \\nu^{-K} e^{ &#8211; \\beta t } \\| u( 0 )\u00a0 \\|_{L^2 ( M) }, \\] where $ \\underline u $ is the (conserved) average of $ u (0) $ with respect to the contact volume form and $K $ is a fixed constant. This provides many examples of very precise {\\em optimal enhanced dissipation} in the sense of recent works of Bedrossian&#8211;Blumenthal&#8211;Punshon-Smith and Elgindi&#8211;Liss&#8211;Mattingly.  The proof is based on results by Dyatlov and the speaker on stochastic stability of Pollicott&#8211;Ruelle resonances,\u00a0 another concept which will be introduced and explained. The talk is based on joint work with Zhongkai Tao. <\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, October 31st&nbsp;will be at&nbsp;3:30pm&nbsp;in&nbsp;Room 740. Speaker: Maciej Zworski Abstract: We consider geodesic flows on negatively curved compact manifolds or more generally contact Anosov flows (all these concepts will be pedagogically explained). The object is to show that if $ X $ is the generator of the flow and $ \\Delta [&hellip;]<\/p>\n","protected":false},"author":87,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-751","post","type-post","status-publish","format-standard","hentry","category-fall-2023"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/751","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\/87"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=751"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/751\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=751"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=751"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=751"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}