{"id":2008,"date":"2026-03-06T19:41:35","date_gmt":"2026-03-06T19:41:35","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/apde\/?p=2008"},"modified":"2026-03-06T19:41:35","modified_gmt":"2026-03-06T19:41:35","slug":"jesus-oliver-cal-state-east-bay","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2026\/03\/06\/jesus-oliver-cal-state-east-bay\/","title":{"rendered":"Jes\u00fas Oliver (Cal State East Bay)"},"content":{"rendered":"<p>The APDE seminar on Monday, 3\/9, will be given by Jes\u00fas Oliver (Cal State East Bay) in-person in <strong>Evans 736,<\/strong>\u00a0and will also be broadcasted online via Zoom from\u00a0<strong>4:10pm to 5:00pm PST<\/strong>. To participate, please email Adam Black (adamblack<span id=\"eeb-322338-403021\"><span id=\"eeb-843318-171438\"><span id=\"eeb-203570-882396\"><span id=\"eeb-990440-551518\"><span id=\"eeb-688663-335757\"><span id=\"eeb-951702-73120\"><span id=\"eeb-183542-482341\"><span id=\"eeb-725178-862757\"><span id=\"eeb-367675-784580\">@berkeley.edu<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<\/p>\n<p><strong>Title<\/strong>: Global existence for a Fritz John equation in expanding FLRW spacetimes<\/p>\n<p><strong>Abstract: <\/strong>We study the semilinear wave equation<\/p>\n<p>\\[\\square_{\\mathbf g_p}\\phi = (\\partial_t \\phi)^2\\]<\/p>\n<p>on expanding FLRW spacetimes with spatial slices $\\mathbb{R}^3$ and power-law scale factor $a(t)=t^p$, where $0 &lt; p \\le 1$. This equation extends the classical Fritz John blow-up model on Minkowski space (the case $p=0$) to a non-stationary cosmological background.<\/p>\n<p>In Minkowski space, nontrivial solutions arising from smooth, compactly supported data blow up in finite time. In contrast, we prove that for $0 &lt; p \\le 1$, sufficiently small, smooth, compactly supported initial data generate global-in-time solutions toward the future.<\/p>\n<p>Earlier joint work with Costa and Franzen treated the accelerated regime $p&gt;1$, where global existence follows from the integrability of the inverse scale factor. In the present setting, this mechanism is unavailable. Instead, we develop a vector field method adapted to FLRW geometry that exploits the interaction between dispersion and spacetime expansion to suppress the nonlinear blow-up mechanism. The argument relies on commuting the Laplace\u2013Beltrami operator with a boosts-free subset of the Poincar\u00e9 algebra and establishing Klainerman\u2013Sideris type estimates adapted to the non-stationary background.<\/p>\n<p>The approach provides a robust framework for quantifying the regularizing effect of cosmological expansion and is expected to extend to a broader class of nonlinear wave equations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 3\/9, will be given by Jes\u00fas Oliver (Cal State East Bay) in-person in Evans 736,\u00a0and will also be broadcasted online via Zoom from\u00a04:10pm to 5:00pm PST. To participate, please email Adam Black (adamblack@berkeley.edu). Title: Global existence for a Fritz John equation in expanding FLRW spacetimes Abstract: We study the semilinear [&hellip;]<\/p>\n","protected":false},"author":119,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2008","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/2008","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\/119"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=2008"}],"version-history":[{"count":2,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/2008\/revisions"}],"predecessor-version":[{"id":2010,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/2008\/revisions\/2010"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=2008"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=2008"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=2008"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}