{"id":1164,"date":"2024-10-18T15:11:52","date_gmt":"2024-10-18T22:11:52","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1164"},"modified":"2024-11-21T17:24:07","modified_gmt":"2024-11-22T01:24:07","slug":"internal-waves-in-a-2d-aquarium","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2024\/10\/18\/internal-waves-in-a-2d-aquarium\/","title":{"rendered":"Internal waves in a 2D aquarium"},"content":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0<strong>October 22th<\/strong>, will be at\u00a0<strong>2<\/strong><strong>:00pm<\/strong>\u00a0in\u00a0<strong>Room 740.<\/strong><\/p>\n<p><strong>Speaker:<\/strong> <a href=\"https:\/\/math.mit.edu\/~zhenhao\/\">Zhenhao Li<\/a><\/p>\n<p style=\"font-weight: 400\"><strong>Abstract: <\/strong>The internal waves equation describes perturbations of a stable-stratified fluid. In an effectively 2D aquarium $\\Omega \\subset \\mathbb{R}^2$, the equation is given by<\/p>\n<p style=\"font-weight: 400\">$ (\\partial_t^2 \\Delta + \\partial_{x_2}^2)u(x, t) = f(x) \\cos(\\lambda t), \\quad t \\ge 0, \\quad x \\in \\Omega$<\/p>\n<p style=\"font-weight: 400\">with Dirichlet boundary conditions. The behavior of the equation is intimately related to the underlying classical dynamics, and Dyatlov-Wang-Zworski proved that for $\\Omega$ with smooth boundary, strong singularities form along the periodic trajectories of the underlying dynamics. Such phenomenon was first experimentally observed in 1997 by Maas-Lam in an aquarium with corners. We will discuss some recent work proving that corners contribute additional mild singularities that propagate according to the dynamics, matching the experimental observations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0October 22th, will be at\u00a02:00pm\u00a0in\u00a0Room 740. Speaker: Zhenhao Li Abstract: The internal waves equation describes perturbations of a stable-stratified fluid. In an effectively 2D aquarium $\\Omega \\subset \\mathbb{R}^2$, the equation is given by $ (\\partial_t^2 \\Delta + \\partial_{x_2}^2)u(x, t) = f(x) \\cos(\\lambda t), \\quad t \\ge 0, \\quad x \\in \\Omega$ [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-1164","post","type-post","status-publish","format-standard","hentry","category-fall-2024"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1164","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\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1164"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1164\/revisions"}],"predecessor-version":[{"id":1165,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1164\/revisions\/1165"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1164"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1164"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}