BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mihaela Ifrim (University of Wisconsin-Madison) DTSTART:20200827T140000Z DTEND:20200827T145000Z DTSTAMP:20260423T035614Z UID:IMS/52 DESCRIPTION:Title: Two dimensional gravity waves at low regularity I: Energy estimates\nby M ihaela Ifrim (University of Wisconsin-Madison) as part of PDE seminar via Zoom\n\n\nAbstract\nThis article represents the first installment of a ser ies of papers concerned with low regularity solutions for the water wave e quations in two space dimensions. Our focus here is on sharp cubic energy estimates. Precisely\, we introduce and develop the techniques to prove a new class of energy estimates\, which we call \\emph{balanced cubic estima tes}. This yields a key improvement over the earlier cubic estimates of Hu nter-Ifrim-Tataru [12]\, while preserving their scale invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using any Strichartz estimates\, these results allow us to si gnificantly lower the Sobolev regularity threshold for local well-posednes s\, drastically improving earlier results obtained by Alazard-Burq-Zuily [ 3\, 4]\, Hunter-Ifrim-Tataru [12] and Ai [2]. This is joint work with Albe rt Ai and Daniel Tataru.\n\nhttps://nguyenquochung1241.wixsite.com/qhung/p ost/pde-seminar-via-zoom\n LOCATION:https://researchseminars.org/talk/IMS/52/ END:VEVENT END:VCALENDAR