{"id":1141,"date":"2022-11-07T15:07:27","date_gmt":"2022-11-07T23:07:27","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=1141"},"modified":"2022-11-07T15:07:27","modified_gmt":"2022-11-07T23:07:27","slug":"leonardo-abbrescia-vanderbilt","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2022\/11\/07\/leonardo-abbrescia-vanderbilt\/","title":{"rendered":"Leonardo Abbrescia (Vanderbilt)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 11\/14, will be given by Leonardo Abbrescia (Vanderbilt) in-person in <strong>Evans 740,<\/strong> and will also be broadcasted online via Zoom from <strong>4:10pm to 5:00pm PST<\/strong>. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu).<\/p>\n\n\n\n<p><strong>Title<\/strong>: A localized picture of the maximal development for shock forming solutions of the 3D compressible Euler equations<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: It is well known that solutions to the inviscid Burgers\u2019 equation form shock singularities in finite time, even when launched from smooth data. A far less documented fact, at least in the popular works on 1D hyperbolic conservation laws, is that shock singularities are intimately tied to a lack-of-uniqueness for the classical Burgers\u2019 equation.<\/p>\n\n\n\n<p>We prove that, locally, solutions to the Compressible Euler equations do not suffer from the same lack-of-uniqueness, even though they can be written as a coupled system of Burgers\u2019 in isentropic plane-symmetry. Roughly, the saving grace is that Euler flow involves&nbsp;two&nbsp;speeds of propagation, and one of them \u201cprevents\u201d the mechanism driving the lack-of-uniqueness. Analytically, this is done by explicitly constructing a portion of the boundary of classical hyperbolic development for shock forming data. This boundary is a connected co-dimension 1 submanifold of Cartesian space, and we will discuss the delicate geo-analytic degeneracies and difficulties involved in its construction. This is joint work with Jared Speck.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 11\/14, will be given by Leonardo Abbrescia (Vanderbilt) in-person in Evans 740, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu). Title: A localized picture of the maximal development for shock forming solutions of the 3D compressible Euler equations Abstract: [&hellip;]<\/p>\n","protected":false},"author":106,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1141","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1141","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\/106"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1141"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1141\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1141"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1141"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}