{"id":1480,"date":"2023-05-10T14:50:38","date_gmt":"2023-05-10T06:50:38","guid":{"rendered":"https:\/\/blog.vanabel.cn\/blog\/2023\/05\/10\/continuous-in-time-bubble-decomposition-for-the-harmonic\/"},"modified":"2023-05-14T00:36:15","modified_gmt":"2023-05-13T16:36:15","slug":"continuous-in-time-bubble-decomposition-for-the-harmonic","status":"publish","type":"post","link":"https:\/\/blog.vanabel.cn\/?p=1480","title":{"rendered":"Continuous in time bubble decomposition for the harmonic&#8230;"},"content":{"rendered":"<p>Continuous in time bubble decomposition for the harmonic map heat flow<br \/>\nJacek Jendrej, Andrew Lawrie, Wilhelm Schlag<br \/>\nWe consider the harmonic map heat flow for maps from the plane to the two-sphere. It is known that solutions to the initial value problem exhibit bubbling along a well-chosen sequence of times. We prove that every sequence of times admits a subsequence along which bubbling occurs. This is deduced as a corollary of our main theorem, which shows that the solution approaches the family of multi-bubble configurations in continuous time.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Continuous in time bubble decomposition for the harmoni&hellip; <a class=\"more-link\" href=\"https:\/\/blog.vanabel.cn\/?p=1480\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">Continuous in time bubble decomposition for the harmonic&#8230;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"status","meta":{"footnotes":""},"categories":[248],"tags":[228,222,229,227,230],"class_list":["post-1480","post","type-post","status-publish","format-status","hentry","category-arxiv","tag-any-time-sequence","tag-blowup","tag-continuous-in-time","tag-harmonic-maps","tag-mustread","post_format-post-format-status","entry"],"_links":{"self":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1480","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1480"}],"version-history":[{"count":1,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1480\/revisions"}],"predecessor-version":[{"id":1494,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1480\/revisions\/1494"}],"wp:attachment":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1480"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1480"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1480"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}