{"id":897,"date":"2020-11-17T16:23:34","date_gmt":"2020-11-18T00:23:34","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=897"},"modified":"2020-11-17T16:23:34","modified_gmt":"2020-11-18T00:23:34","slug":"khang-manh-huynh-ucla","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2020\/11\/17\/khang-manh-huynh-ucla\/","title":{"rendered":"Khang Manh Huynh (UCLA)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 11\/30, will be given by Khang Manh Huynh  online via Zoom from\u00a0<strong>4:10 to 5:00pm<\/strong>. To participate, email Georgios Moschidis (gmoschidis@berkeley.edu) or Federico Pasqualotto (fpasqualotto@berkeley.edu).<\/p>\n\n\n\n<p>Title: Construction of the Hodge-Neumann heat kernel, local Bernstein estimates, and Onsager&#8217;s conjecture in fluid dynamics.<\/p>\n\n\n\n<p>Abstract: Most recently, in arXiv:1907.05360 [math.AP], we introduced the theory of heatable currents and proved Onsager&#8217;s conjecture on Riemannian manifolds with boundary, where the weak solution has $B_{3,1}^{\\frac{1}{3}}$ spatial regularity. In this sequel, by applying techniques from geometric microlocal analysis to construct the Hodge-Neumann heat kernel, we obtain off-diagonal decay and local Bernstein estimates, and then use them to extend the result to the Besov space $\\widehat{B}_{3,V}^{\\frac{1}{3}}$, which generalizes both the space $\\widehat{B}_{3,c(\\mathbb{N})}^{1\/3}$ from arXiv:1310.7947 [math.AP] and the space $\\underline{B}_{3,\\text{VMO}}^{1\/3}$ from arXiv:1902.07120 [math.AP] &#8212; the best known function space where Onsager&#8217;s conjecture holds on flat backgrounds.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 11\/30, will be given by Khang Manh Huynh online via Zoom from\u00a04:10 to 5:00pm. To participate, email Georgios Moschidis (gmoschidis@berkeley.edu) or Federico Pasqualotto (fpasqualotto@berkeley.edu). Title: Construction of the Hodge-Neumann heat kernel, local Bernstein estimates, and Onsager&#8217;s conjecture in fluid dynamics. Abstract: Most recently, in arXiv:1907.05360 [math.AP], we introduced the theory [&hellip;]<\/p>\n","protected":false},"author":110,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-897","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/897","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\/110"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=897"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/897\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=897"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=897"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=897"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}