{"id":1603,"date":"2026-03-26T23:41:36","date_gmt":"2026-03-27T06:41:36","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1603"},"modified":"2026-04-14T20:05:01","modified_gmt":"2026-04-15T03:05:01","slug":"late-time-tails-of-the-einstein-vacuum-equation-near-minkowski-spacetime-in-wave-gauges","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2026\/03\/26\/late-time-tails-of-the-einstein-vacuum-equation-near-minkowski-spacetime-in-wave-gauges\/","title":{"rendered":"Late-time tails of the Einstein vacuum equation near Minkowski spacetime in wave gauges"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <strong>March 31th<\/strong>, will be at\u00a0<strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:\u00a0<\/strong>Yuchen Mao<\/p>\n<p><strong>Abstract:\u00a0<\/strong>It has been expected that wave gauges lead to weak time decay of solutions of the Einstein vacuum equation near Minkowski spacetime, even though Lindblad-Rodnianski used the standard wave gauge to prove global nonlinear stability of Minkowski spacetime in their renowned work. Lindblad further observed the weak $\\tau^{-1}$ decay by identifying the source of the time asymptotics. In this talk, I will introduce a new result that proves i) the late time tail; i.e. the leading term in the time asymptotic expansion, is indeed $\\tau^{-1}$ in the standard wave gauge, and ii) by slightly modifying the wave gauge condition, one can achieve decay better than $\\tau^{-1}$, hence better than expected before. The proof adapts the iteration scheme developed in Luk-Oh to the weak null system of wave equations under wave gauges in order to identify the tail, and chooses the wave gauge so that the zeroth spherical harmonic in the semilinear weak null structure that causes the weak decay is canceled.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, March 31th, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Yuchen Mao Abstract:\u00a0It has been expected that wave gauges lead to weak time decay of solutions of the Einstein vacuum equation near Minkowski spacetime, even though Lindblad-Rodnianski used the standard wave gauge to prove global nonlinear stability of Minkowski spacetime in their renowned work. [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26,1],"tags":[],"class_list":["post-1603","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\/1603","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\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1603"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1603\/revisions"}],"predecessor-version":[{"id":1604,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1603\/revisions\/1604"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}