{"id":1207,"date":"2023-04-10T17:29:40","date_gmt":"2023-04-11T00:29:40","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=1207"},"modified":"2023-04-10T17:29:40","modified_gmt":"2023-04-11T00:29:40","slug":"kihyun-kim","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2023\/04\/10\/kihyun-kim\/","title":{"rendered":"Kihyun Kim (IHES)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 4\/17, will be given by Kihyun Kim in-person in&nbsp;<strong>Evans 732,<\/strong>&nbsp;and will also be broadcasted online via Zoom from&nbsp;<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\n\n\n<p><strong>Title:<\/strong> Rigidity of long-term dynamics for the self-dual Chern-Simons-Schr\u00f6dinger equation within equivariance<\/p>\n\n\n\n<p><strong>Abstract:<\/strong> We consider the long time dynamics for the self-dual Chern-Simons-Schr\u00f6dinger equation (CSS) within equivariant symmetry. Being a gauged 2D cubic nonlinear Schr\u00f6dinger equation (NLS), (CSS) is L2-critical and has pseudoconformal invariance and solitons. However, there are two distinguished features of (CSS), the self-duality and non-locality, which make the long time dynamics of (CSS) surprisingly rigid. For instance, (i) any finite energy spatially decaying solutions to (CSS) decompose into at most one(!) modulated soliton and a radiation. Moreover, (ii) in the high equivariance case (i.e., the equivariance index \u2265 1), any smooth finite-time blow-up solutions even have a universal blow-up speed, namely, the pseudoconformal one. We explore this rigid dynamics using modulation analysis, combined with the self-duality and non-locality of the problem.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 4\/17, will be given by Kihyun Kim in-person in&nbsp;Evans 732,&nbsp;and will also be broadcasted online via Zoom from&nbsp;4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu). Title: Rigidity of long-term dynamics for the self-dual Chern-Simons-Schr\u00f6dinger equation within equivariance Abstract: We consider the long time [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1207","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1207","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=1207"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1207\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1207"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1207"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1207"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}