{"id":485,"date":"2022-04-04T09:16:13","date_gmt":"2022-04-04T16:16:13","guid":{"rendered":"\/wp\/hades\/?p=485"},"modified":"2022-04-04T09:16:13","modified_gmt":"2022-04-04T16:16:13","slug":"galilean-theory-of-dispersion-and-scattering-conservation-laws-blind-cones-and-the-increase-of-uncertainty","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2022\/04\/04\/galilean-theory-of-dispersion-and-scattering-conservation-laws-blind-cones-and-the-increase-of-uncertainty\/","title":{"rendered":"Galilean Theory of Dispersion and Scattering:  Conservation laws, Blind Cones and the Increase of Uncertainty"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday,\u00a0<strong>April 5<\/strong>\u00a0will be at\u00a0<strong>3:30 pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n\n\n\n<p><strong>Speaker<\/strong>: Nima Moini<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: In this talk, I will sketch a new approach to the study of kinetic equations solely under the assumption of conservation laws.\u00a0The new idea is based on an uncertainty principle, the introduction of blind cones with respect to an observer and the Galilean invariance of different inertial frames of reference.\u00a0In fact, as the uncertainty inevitably increases with time, particles will move away in an asymptotically radial manner from any fixed observer thereby establishing a new notion of dispersion.\u00a0The generality of this approach reveals a mathematical relationship between the Landau and Boltzmann equations in the context of &#8220;the grazing collisions&#8221;, which until now was solely phenomenological.\u00a0Moreover, I will discuss a new scattering theory for the kinetic equations and demonstrate its utility in the case of the Boltzmann equation for hard spheres.\u00a0The new framework improves upon the existing results by proving the asymptotic completeness of the solutions of the Boltzmann equation near an equilibrium in the\u00a0 $L^\\infty$ setting.\u00a0In particular, for any solution to the transport equation, there are arbitrarily close in $L^\\infty$\u00a0 norm, scattered solutions of the Boltzmann equation, this implies that solutions of the Boltzmann equation defined over the whole space will not converge to the state of thermodynamic\u00a0equilibrium.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0April 5\u00a0will be at\u00a03:30 pm\u00a0in\u00a0Room 740. Speaker: Nima Moini Abstract: In this talk, I will sketch a new approach to the study of kinetic equations solely under the assumption of conservation laws.\u00a0The new idea is based on an uncertainty principle, the introduction of blind cones with respect to an observer and [&hellip;]<\/p>\n","protected":false},"author":91,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-485","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/485","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\/91"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=485"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/485\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}