BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yu Deng (University of Southern California) DTSTART:20200430T150000Z DTEND:20200430T155000Z DTSTAMP:20260423T021117Z UID:IMS/9 DESCRIPTION:Title: Deri vation of the wave kinetic equation\nby Yu Deng (University of Souther n California) as part of PDE seminar via Zoom\n\n\nAbstract\nThe wave turb ulence theory describes the nonequilibrium statistical mechanics for a lar ge class of nonlinear dispersive systems. A major goal of this theory is t o derive the wave kinetic equation\, which predicts the behavior of macros copic limits of ensemble averages for microscopic interacting systems. Usu ally this limit happens at a particular "kinetic time scale" in the "weak- nonlinearity" limit where the number of interacting modes goes to infinity while the nonlinearity strength goes to zero. For nonlinear Schrodinger e quations such limits have been derived on a formal level and studied exten sively since the 1920s\, but a rigorous proof remains open.\n\n\nIn this w ork\, joint with Zaher Hani\, we provide the first rigorous derivation of wave kinetic equation\, which reaches the kinetic time scale up to an arbi trary small power\, in a particular scaling regime for the number of modes and the strength of nonlinearity. We rely on a robust method\, which can be extended to other semilinear models\, and possibly also to quasilinear models (such as water waves).\n LOCATION:https://researchseminars.org/talk/IMS/9/ END:VEVENT END:VCALENDAR