{"id":1590,"date":"2026-03-06T09:42:27","date_gmt":"2026-03-06T17:42:27","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1590"},"modified":"2026-03-09T15:38:44","modified_gmt":"2026-03-09T22:38:44","slug":"existence-of-weak-solutions-to-a-model-of-the-geodynamo","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2026\/03\/06\/existence-of-weak-solutions-to-a-model-of-the-geodynamo\/","title":{"rendered":"Existence of weak solutions to a model of the geodynamo"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <strong>March 10th<\/strong>, will be at\u00a0<strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:\u00a0<\/strong>Tom Schang<\/p>\n<p><strong>Abstract:\u00a0<\/strong>In this talk, I will discuss a model of the earth\u2019s magnetic field that has previously been simulated numerically, but has not been shown to be well-posed. This model couples solid physics for the electrically conducting inner core with magnetohydrodynamic (MHD) equations in the liquid outer core, as well as the magnetic field outside of the core, which is taken to be non-conducting. I will define and prove existence of Leray-Hopf-type weak solutions for this system. Particular challenges include the transmission conditions of the magnetic field coming from non-constant physical parameters and extending the magnetic field to a non-conducting exterior. To address these problems, we must carefully define a function space and prove appropriate embeddings.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, March 10th, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Tom Schang Abstract:\u00a0In this talk, I will discuss a model of the earth\u2019s magnetic field that has previously been simulated numerically, but has not been shown to be well-posed. This model couples solid physics for the electrically conducting inner core with magnetohydrodynamic (MHD) equations [&hellip;]<\/p>\n","protected":false},"author":121,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26,1],"tags":[],"class_list":["post-1590","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\/1590","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\/121"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1590"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1590\/revisions"}],"predecessor-version":[{"id":1591,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1590\/revisions\/1591"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1590"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1590"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}