BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Julian Fischer (Institute of Science and Technology Austria (IST A ustria)) DTSTART:20200521T150000Z DTEND:20200521T155000Z DTSTAMP:20260423T052545Z UID:IMS/20 DESCRIPTION:Title: Wea k-strong uniqueness principles for interface evolution problems in fluid m echanics and geometry\nby Julian Fischer (Institute of Science and Tec hnology Austria (IST Austria)) as part of PDE seminar via Zoom\n\n\nAbstra ct\nIn evolution equations for interfaces\, topological changes and geomet ric singularities occur naturally\, one basic example being the pinchoff o f liquid droplets. As a consequence\, classical solution concepts for such PDEs are naturally limited to short-time existence results or particular initial configurations like perturbations of a steady state. At the same t ime\, the transition from strong to weak solution concepts for PDEs is pro ne to incurring unphysical non-uniqueness of solutions. In the absence of a comparison principle\, the relation between weak solution concepts and s trong solution concepts for interface evolution problems has remained a mo stly open question. We establish weak-strong uniqueness principles for two important interface evolution problems\, namely for planar multiphase mea n curvature flow and for the evolution of the free boundary between two vi scous fluids: As long as a classical solution to these evolution problems exists\, it is also the unique BV solution respectively varifold solution. In the case of multiphase mean curvature flow\, our construction leads to a gradient-flow analogue of the notion of calibrations.\n\nBased on joint works with Sebastian Hensel\, Tim Laux\, and Thilo Simon.\n\nHere is the poster of this talk: https://www.dropbox.com/s/807vg0v0nrmlp2d/PDE%20Semin ar%207th.pdf?dl=0\nPlease visit our website to get more information: nguye nquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n LOCATION:https://researchseminars.org/talk/IMS/20/ END:VEVENT END:VCALENDAR