{"id":903,"date":"2024-05-06T14:47:50","date_gmt":"2024-05-06T21:47:50","guid":{"rendered":"\/wp\/hades\/?p=903"},"modified":"2024-05-06T14:47:50","modified_gmt":"2024-05-06T21:47:50","slug":"analysis-of-micro-and-macro-scale-models-of-superfluidity","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2024\/05\/06\/analysis-of-micro-and-macro-scale-models-of-superfluidity\/","title":{"rendered":"Analysis of micro- and macro-scale models of superfluidity"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday, <strong>May 7th<\/strong>, will be at <strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 748.<\/strong><\/p>\n\n\n\n<p><strong>Speaker:<\/strong> <a href=\"https:\/\/sites.google.com\/view\/pcjayanti\/home?authuser=0\">Pranava Jayanti<\/a><\/p>\n\n\n\n<p><strong>Abstract:<\/strong> We introduce the physics of superfluidity, including two  mathematical models. We begin with a micro-scale description of the  interacting dynamics between the superfluid and normal fluid phases of  Helium-4 at length scales much smaller than the inter-vortex spacing.  This system consists of the nonlinear Schr\u00f6dinger equation and the  incompressible, inhomogeneous Navier-Stokes equations, coupled to each  other via a bidirectional nonlinear relaxation mechanism. The coupling  permits mass\/momentum\/energy transfer between the phases, and accounts  for the conversion of superfluid into normal fluid. We prove the  existence of solutions in $\\mathbb{T}^n$ (for n=2,3) for a power-type  nonlinearity, beginning from small initial data. Depending upon the  strength of the nonlinear self-interactions, we obtain solutions that  are global or almost-global in time. The main challenge is to control  the inter-phase mass transfer in order to ensure the strict positivity  of the normal fluid density, while deriving time-independent a priori  estimates. We compare two different approaches: purely energy based,  versus a combination of energy estimates and maximal regularity. The  results are from recent collaborations with Juhi Jang and Igor Kukavica.<br>We  will also briefly discuss some results pertaining to a macro-scale  model known as the HVBK equations, some of which is joint work with  Konstantina Trivisa.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, May 7th, will be at 3:30pm\u00a0in\u00a0Room 748. Speaker: Pranava Jayanti Abstract: We introduce the physics of superfluidity, including two mathematical models. We begin with a micro-scale description of the interacting dynamics between the superfluid and normal fluid phases of Helium-4 at length scales much smaller than the inter-vortex spacing. This [&hellip;]<\/p>\n","protected":false},"author":92,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-903","post","type-post","status-publish","format-standard","hentry","category-spring-2024"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/903","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\/92"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=903"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/903\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}