{"id":1834,"date":"2025-04-15T03:08:36","date_gmt":"2025-04-15T03:08:36","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/apde\/?p=1834"},"modified":"2025-04-16T19:53:32","modified_gmt":"2025-04-16T19:53:32","slug":"ovidiu-neculai-avadanei-uc-berkeley","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2025\/04\/15\/ovidiu-neculai-avadanei-uc-berkeley\/","title":{"rendered":"Ovidiu-Neculai Avadanei (UC Berkeley)"},"content":{"rendered":"<div class=\"entry-content\">\n<div class=\"entry-content\">\n<div class=\"entry-content\">\n<p>The APDE seminar on Monday, <span data-sheets-root=\"1\">4\/21<\/span>, will be given by Ovidiu-Neculai Avadanei (UC Berkeley) in-person in <strong>Evans 736,<\/strong> and will also be broadcasted online via Zoom from <strong>4:10pm to 5:00pm PDT<\/strong>. To participate, please email Robert Schippa (<span id=\"eeb-322338-403021\"><span id=\"eeb-843318-171438\"><span id=\"eeb-203570-882396\"><span id=\"eeb-990440-551518\"><span id=\"eeb-688663-335757\">rschippa@berkeley.edu<\/span><\/span><\/span><\/span><\/span>).<\/p>\n<p><strong>Title:<\/strong> Counterexamples to Strichartz estimates and gallery waves for the irrotational compressible Euler equation in a vacuum setting.<\/p>\n<p><strong>Abstract: <\/strong>We consider the free boundary problem for the irrotational compressible Euler equation in a vacuum setting. By using the irrotationality condition in the Eulerian formulation of Ifrim and Tataru, we derive a formulation of the problem in terms of the velocity potential function, which turns out to be an acoustic wave equation that is widely used in solar seismology. This paper is a first step towards understanding what Strichartz estimates are achievable for the aforementioned equation. Our object of study is the corresponding linearized problem in a model case, in which our domain is represented by the upper half-space. For this, we investigate the geodesics corresponding to the resulting acoustic metric, which have multiple periodic reflections next to the boundary. Inspired by their dynamics, we define a class of whispering gallery type modes associated to our problem, and prove Strichartz estimates for them. By using a construction akin to a wave packet, we also prove that one necessarily has a loss of derivatives in the Strichartz estimates for the acoustic wave equation satisfied by the potential function. In particular, this suggests that the low regularity well-posedness result obtained by Ifrim and Tataru might be optimal, at least in a certain frequency regime. To the best of our knowledge, these are the first results of this kind for the<br \/>\nirrotational vacuum compressible Euler equations.<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 4\/21, will be given by Ovidiu-Neculai Avadanei (UC Berkeley) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PDT. To participate, please email Robert Schippa (rschippa@berkeley.edu). Title: Counterexamples to Strichartz estimates and gallery waves for the irrotational compressible Euler equation in a vacuum [&hellip;]<\/p>\n","protected":false},"author":112,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1834","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1834","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\/112"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1834"}],"version-history":[{"count":3,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1834\/revisions"}],"predecessor-version":[{"id":1839,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1834\/revisions\/1839"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1834"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1834"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}