{"id":1574,"date":"2026-02-20T22:06:36","date_gmt":"2026-02-21T06:06:36","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1574"},"modified":"2026-03-09T15:38:29","modified_gmt":"2026-03-09T22:38:29","slug":"enhanced-lifespan-bounds-for-1d-quasilinear-klein-gordon-flows","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2026\/02\/20\/enhanced-lifespan-bounds-for-1d-quasilinear-klein-gordon-flows\/","title":{"rendered":"Enhanced lifespan bounds for 1D quasilinear Klein-Gordon flows"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <b>February 24th<\/b>, will be at <strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:\u00a0<\/strong>Hongjing Huang<\/p>\n<p><strong>Abstract:<\/strong><\/p>\n<div><span data-removefontsize=\"true\" data-originalcomputedfontsize=\"16\">We consider one-dimensional scalar quasilinear Klein&#8211;Gordon equations with general nonlinearities, on both $\\mathbb R$ and $\\mathbb T$.<\/span><\/div>\n<div><span data-removefontsize=\"true\" data-originalcomputedfontsize=\"16\">By employing a refined modified-energy framework of Ifrim and Tataru, we investigate long time lifespan bounds for small data solutions.<\/span><\/div>\n<div><span data-removefontsize=\"true\" data-originalcomputedfontsize=\"16\">Our main result asserts \u00a0that solutions with small initial data of size $\\epsilon$ persist on the improved cubic timescale $|t| \\lesssim \\epsilon^{-2}$ and satisfy sharp cubic energy estimates throughout this interval. We also establish difference bounds on the same time scale. In the case\u00a0<\/span><\/div>\n<div><span data-removefontsize=\"true\" data-originalcomputedfontsize=\"16\">of $\\mathbb R$, we are further able\u00a0<\/span><\/div>\n<div><span data-removefontsize=\"true\" data-originalcomputedfontsize=\"16\">to use dispersion in order to extend the lifespan to $\\epsilon^{-4}$. This generalizes earlier results\u00a0<\/span><\/div>\n<div><span data-removefontsize=\"true\" data-originalcomputedfontsize=\"16\">obtained by Delort, \\cite{Delort1997_KG1D} \u00a0in the semilinear case.<\/span><\/div>\n<div><\/div>\n<div>This joint work with Mihaela Ifrim and Daniel Tataru.<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, February 24th, will be at 3:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Hongjing Huang Abstract: We consider one-dimensional scalar quasilinear Klein&#8211;Gordon equations with general nonlinearities, on both $\\mathbb R$ and $\\mathbb T$. By employing a refined modified-energy framework of Ifrim and Tataru, we investigate long time lifespan bounds for small data solutions. Our main result [&hellip;]<\/p>\n","protected":false},"author":121,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26,1],"tags":[],"class_list":["post-1574","post","type-post","status-publish","format-standard","hentry","category-spring-2026","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1574","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/121"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1574"}],"version-history":[{"count":3,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1574\/revisions"}],"predecessor-version":[{"id":1580,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1574\/revisions\/1580"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1574"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1574"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1574"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}