{"id":2041,"date":"2026-09-08T22:09:33","date_gmt":"2026-09-08T22:09:33","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/apde\/?p=2041"},"modified":"2026-09-08T22:09:33","modified_gmt":"2026-09-08T22:09:33","slug":"ovidiu-neculai-avadanei-caltech","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2026\/09\/08\/ovidiu-neculai-avadanei-caltech\/","title":{"rendered":"Ovidiu-Neculai Avadanei (Caltech)"},"content":{"rendered":"<p>The APDE seminar on Monday, 9\/14, will be given by Ovidiu-Neculai Avadanei (Caltech) 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>: A conditional Lagrangian clock barrier at the $C^{1,\\frac{1}{3}}$ threshold for axisymmetric Euler without swirl<\/p>\n<p><strong>Abstract: \u00a0<\/strong>We consider axisymmetric no-swirl solutions to the three-dimensional incompressible Euler equations, with initial velocity in $C^{1,\\alpha}\\cap L^2$, where $\\alpha\\in\\left[\\frac{1}{3},1\\right)$. In a major breakthrough, Shkoller introduced a clock-and-driver framework that he used in order to prove finite-time type I blow-up below the $C^{1,\\frac{1}{3}}$ threshold. Motivated by this, we define Lagrangian classes of coherent initial data and conditional solutions for which the same mechanism yields a supercritical-critical barrier to blow-up when $\\alpha\\geq\\frac{1}{3}$. When $\\alpha&gt;\\frac{1}{3}$, the aforementioned barrier is genuinely depleted, whereas at the critical endpoint $\\alpha=\\frac{1}{3}$, we obtain an exponential bound preventing blow-up. In the general case, we formulate a matrix-clock criterion in terms of the smallest singular value of the deformation gradient and show that, under cusp-tail, Dini coherence, near-field compatibility, and bounded transverse-distortion hypotheses, this singular value cannot collapse in finite time. In the on-axis case, the criterion reduces to the scalar clock inequality $\\displaystyle \\dot{J}(t)\\gtrsim -B(t)J(t)-CJ(t)^{3\\alpha}$, which rules out Shkoller-type clock collapse for $\\alpha\\geq\\frac{1}{3}$. These results do not enlarge the known Lorentz-space global regularity classes. Rather, they in particular identify the supercritical Lagrangian obstruction dual to Shkoller&#8217;s subcritical blow-up mechanism in the case $\\alpha&gt;\\frac{1}{3}$.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 9\/14, will be given by Ovidiu-Neculai Avadanei (Caltech) 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: A conditional Lagrangian clock barrier at the $C^{1,\\frac{1}{3}}$ threshold for axisymmetric Euler without swirl Abstract: \u00a0We consider axisymmetric no-swirl [&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-2041","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/2041","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=2041"}],"version-history":[{"count":2,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/2041\/revisions"}],"predecessor-version":[{"id":2043,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/2041\/revisions\/2043"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=2041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=2041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=2041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}