{"id":1684,"date":"2024-09-16T06:08:52","date_gmt":"2024-09-16T06:08:52","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/apde\/?p=1684"},"modified":"2024-09-16T06:08:52","modified_gmt":"2024-09-16T06:08:52","slug":"anuj-kumar-uc-berkeley","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2024\/09\/16\/anuj-kumar-uc-berkeley\/","title":{"rendered":"Anuj Kumar (UC Berkeley)"},"content":{"rendered":"<p>The APDE seminar on Monday, 9\/23, will be given by Anuj Kumar (UC Berkeley) 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, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).<\/p>\n<p><strong>Title<\/strong>: Nonuniqueness of solutions to the Euler equations with integrable vorticity<\/p>\n<p><strong>Abstract<\/strong>: Yudovich established the well-posedness of the two-dimensional incompressible Euler equations for solutions with bounded vorticity. DiPerna and Majda proved the existence of weak solutions with vorticity in L^p ( p &gt; 1).\u00a0 A celebrated open question is whether the uniqueness result can be generalized to solutions with L^p vorticity. In this talk, we resolve this question in negative for some p &gt; 1. To prove nonuniqueness, we devise a new convex integration scheme that employs non-periodic, spatially-anisotropic perturbations, an idea that was inspired by our recent work on the transport equation. To construct the perturbation, we introduce a new family of building blocks based on the Lamb-Chaplygin dipole. This is a joint work with Elia Bru\u00e8 and Maria Colombo.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 9\/23, will be given by Anuj Kumar (UC Berkeley) in-person in Evans 740, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu). Title: Nonuniqueness of solutions to the Euler equations with integrable vorticity Abstract: Yudovich [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1684","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1684","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\/102"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1684"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1684\/revisions"}],"predecessor-version":[{"id":1685,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1684\/revisions\/1685"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1684"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1684"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1684"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}