BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sijue Wu/邬思珏 (University of Michigan) DTSTART:20201227T030000Z DTEND:20201227T040000Z DTSTAMP:20260423T040335Z UID:iccm2020/3 DESCRIPTION:Title: The Quartic Integrability and Long Time Existence of Steep Water Waves in 2d\nby Sijue Wu/邬思珏 (University of Michigan) as part of ICCM 20 20\n\n\nAbstract\nIt is known since the work of Dyachenko & Zakharov in 19 94 that for the weakly nonlinear 2d infinite depth water waves\, there are no 3-wave interactions and all of the 4-wave interaction coefficients van ish on the resonant manifold. In this talk I will present a recent result that proves this partial integrability from a different angle. We construc t a sequence of energy functionals Ej (t)\, directly in the physical space \, that involves material derivatives of order j of the solutions for the 2d water wave equation\, so that d dtEj (t) is quintic or higher order. We show that if some scaling invariant norm\, and a norm involving one speci al derivative above the scaling of the initial data are of size no more th an ε\, then the lifespan of the solution for the 2d water wave equation i s at least of order O(ε−3 )\, and the solution remains as regular as th e initial data during this time. If only the scaling invariant norm of the data is of size ε\, then the lifespan of the solution is at least of ord er O(ε−5/2 ). Our long time existence results do not impose size restri ctions on the slope of the initial interface and the magnitude of the init ial velocity\, they allow the interface to have arbitrary large steepnesse s and initial velocities to have arbitrary large magnitudes.\n LOCATION:https://researchseminars.org/talk/iccm2020/3/ END:VEVENT END:VCALENDAR