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SUMMARY:Yu Deng (University of Southern California)
DTSTART:20200430T150000Z
DTEND:20200430T155000Z
DTSTAMP:20260404T164920Z
UID:IMS/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IMS/9
 /">Derivation of the wave kinetic equation</a>\nby Yu Deng (University of 
 Southern California) as part of PDE seminar via Zoom\n\n\nAbstract\nThe wa
 ve turbulence theory describes the nonequilibrium statistical mechanics fo
 r a large class of nonlinear dispersive systems. A major goal of this theo
 ry is to derive the wave kinetic equation\, which predicts the behavior of
  macroscopic limits of ensemble averages for microscopic interacting syste
 ms. Usually this limit happens at a particular "kinetic time scale" in the
  "weak-nonlinearity" limit where the number of interacting modes goes to i
 nfinity while the nonlinearity strength goes to zero. For nonlinear Schrod
 inger equations such limits have been derived on a formal level and studie
 d extensively since the 1920s\, but a rigorous proof remains open.\n\n\nIn
  this work\, joint with Zaher Hani\, we provide the first rigorous derivat
 ion of wave kinetic equation\, which reaches the kinetic time scale up to 
 an arbitrary small power\, in a particular scaling regime for the number o
 f modes and the strength of nonlinearity. We rely on a robust method\, whi
 ch can be extended to other semilinear models\, and possibly also to quasi
 linear models (such as water waves).\n
LOCATION:https://stable.researchseminars.org/talk/IMS/9/
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