{"id":911,"date":"2021-02-02T17:23:40","date_gmt":"2021-02-03T01:23:40","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=911"},"modified":"2021-02-02T17:23:40","modified_gmt":"2021-02-03T01:23:40","slug":"kihyun-kim-kaist","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2021\/02\/02\/kihyun-kim-kaist\/","title":{"rendered":"Kihyun Kim (KAIST)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 2\/8, will be given by Kihyun Kim online via Zoom from\u00a0<strong>4:10 to 5:00pm<\/strong>. To participate, email Georgios Moschidis (gmoschidis@berkeley.edu) or Federico Pasqualotto (fpasqualotto@berkeley.edu).<\/p>\n\n\n\n<p>Title: Blow-up dynamics for the self-dual Chern-Simons-Schr\u00f6dinger equation<\/p>\n\n\n\n<p>Abstract: We consider the blow-up dynamics for the self-dual Chern-Simons-Schr\u00f6dinger equation (CSS) under equivariance symmetry. (CSS) is $L^2$-critical, has the pseudoconformal symmetry, and admits a soliton $Q$ for each equivariance index $m \\geq 0$. An application of the pseudoconformal transformation to $Q$ yields an explicit finite-time blow-up solution $S(t)$ which contracts at the pseudoconformal rate $|t|$. In the high equivariance case $m \\geq 1$, the pseudoconformal blow-up for smooth finite energy solutions in fact occurs in a codimension one sense, but also exhibits an instability mechanism. In the radial case $m=0$, however, $S(t)$ is no longer a finite energy blow-up solution. Interestingly enough, there are smooth finite energy blow-up solutions whose blow-up rates differ from the pseudoconformal rate by a power of logarithm. We will explore these interesting blow-up dynamics (with more focus on the latter) via modulation analysis. This talk is based on my joint works with Soonsik Kwon and Sung-Jin Oh.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 2\/8, will be given by Kihyun Kim online via Zoom from\u00a04:10 to 5:00pm. To participate, email Georgios Moschidis (gmoschidis@berkeley.edu) or Federico Pasqualotto (fpasqualotto@berkeley.edu). Title: Blow-up dynamics for the self-dual Chern-Simons-Schr\u00f6dinger equation Abstract: We consider the blow-up dynamics for the self-dual Chern-Simons-Schr\u00f6dinger equation (CSS) under equivariance symmetry. (CSS) is $L^2$-critical, has [&hellip;]<\/p>\n","protected":false},"author":110,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-911","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/911","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\/110"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=911"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/911\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=911"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=911"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}