{"id":1274,"date":"2025-03-07T14:14:22","date_gmt":"2025-03-07T22:14:22","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1274"},"modified":"2025-05-04T19:35:34","modified_gmt":"2025-05-05T02:35:34","slug":"wellposedness-of-the-electron-mhd-without-resistivity-for-large-perturbations-of-the-uniform-magnetic-field","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2025\/03\/07\/wellposedness-of-the-electron-mhd-without-resistivity-for-large-perturbations-of-the-uniform-magnetic-field\/","title":{"rendered":"Wellposedness of the electron MHD without resistivity for large perturbations of the uniform magnetic field"},"content":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0<strong>March<\/strong><strong> 18th<\/strong>, will be at\u00a0<strong>3<\/strong><strong>:30pm<\/strong>\u00a0in\u00a0<strong>Room 740.<\/strong><\/p>\n<p><strong>Speaker:\u00a0<\/strong>Sung-Jin Oh<\/p>\n<p><strong>Abstract: <\/strong>The electron magnetohydrodynamics equation (E-MHD) is a fluid description of plasma in small scales where the motion of electrons relative to ions is significant. Mathematically, (E-MHD) is a quasilinear dispersive equation with nondegenerate but nonelliptic second-order principal term. In this talk, I&#8217;ll discuss a recent proof, joint with In-Jee Jeong, of the local wellposedness of the Cauchy problems for (E-MHD) without resistivity for possibly large perturbations of nonzero uniform magnetic fields. While the local wellposedness problem for (E-MHD) has been extensively studied in the presence of resistivity (which provides dissipative effects), this seems to be the first such result without resistivity.<\/p>\n<p>More specifically, my goal is to explain the main new ideas introduced in this work and the related work of Pineau-Taylor on quasilinear ultrahyperbolic Schrodinger equations, which also have nondegenerate but nonelliptic principal terms. Both works significantly improve upon the classical work of Kenig-Ponce-Rolvung-Vega on such PDEs, in the sense that the regularity and decay assumptions on the initial data are greatly weakened to the level analogous to the recent work of Marzuola-Metcalfe-Tataru in the case of an elliptic principal term.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0March 18th, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Sung-Jin Oh Abstract: The electron magnetohydrodynamics equation (E-MHD) is a fluid description of plasma in small scales where the motion of electrons relative to ions is significant. Mathematically, (E-MHD) is a quasilinear dispersive equation with nondegenerate but nonelliptic second-order principal term. In this talk, I&#8217;ll [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22,1],"tags":[],"class_list":["post-1274","post","type-post","status-publish","format-standard","hentry","category-spring-2025","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1274","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\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1274"}],"version-history":[{"count":2,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1274\/revisions"}],"predecessor-version":[{"id":1282,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1274\/revisions\/1282"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1274"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1274"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}