{"id":1452,"date":"2025-10-11T21:13:31","date_gmt":"2025-10-12T04:13:31","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1452"},"modified":"2025-10-11T21:13:31","modified_gmt":"2025-10-12T04:13:31","slug":"dissipation-estimates-of-the-fisher-information-for-the-landau-equation","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2025\/10\/11\/dissipation-estimates-of-the-fisher-information-for-the-landau-equation\/","title":{"rendered":"Dissipation estimates of the Fisher information for the Landau equation"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <strong>October<\/strong><strong> 21st<\/strong>, will be at <strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:\u00a0<\/strong>Sehyun Ji<\/p>\n<p><strong>Abstract: <\/strong>The global existence of smooth solution for the Landau-Coulomb equation remained elusive for a long time. Two years ago, Nestor Guillen and Luis Silvestre made a breakthrough by showing the\u00a0Fisher\u00a0information\u00a0is monotone decreasing. As a consequence, they deduced the solutions do not blow up for C^1 initial data with Maxwellian tails. For a monotone quantity, It is very natural to ask for its dissipation estimate. In this talk, I will derive an a priori estimate for the dissipation of the\u00a0Fisher\u00a0information, which appears to be\u00a0a higher-order analogue of the entropy dissipation estimate. As an application, I&#8217;ll show the global existence of smooth solutions for rough initial data in L^1_5 \\cap L \\log L. I will start from discussing the proof of Guillen and Silvestre.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, October 21st, will be at 3:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Sehyun Ji Abstract: The global existence of smooth solution for the Landau-Coulomb equation remained elusive for a long time. Two years ago, Nestor Guillen and Luis Silvestre made a breakthrough by showing the\u00a0Fisher\u00a0information\u00a0is monotone decreasing. As a consequence, they deduced the solutions do [&hellip;]<\/p>\n","protected":false},"author":116,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25],"tags":[],"class_list":["post-1452","post","type-post","status-publish","format-standard","hentry","category-fall-2025"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1452","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\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1452"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1452\/revisions"}],"predecessor-version":[{"id":1453,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1452\/revisions\/1453"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1452"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1452"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}