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SUMMARY:Zaher Hani (University of Michigan)
DTSTART:20210520T130000Z
DTEND:20210520T135000Z
DTSTAMP:20260423T035635Z
UID:IMS/81
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/81/">Ful
 l derivation of the wave kinetic equation</a>\nby Zaher Hani (University o
 f Michigan) as part of PDE seminar via Zoom\n\n\nAbstract\nWe will discuss
  a recent work\, in collaboration with Yu Deng (USC)\, in which we provide
  the rigorous derivation of the wave kinetic equation from the cubic nonli
 near Schrödinger (NLS) equation at the kinetic timescale\, under a partic
 ular scaling law that describes the limiting process. This solves a main c
 onjecture in the theory of wave turbulence\, i.e. the kinetic theory of no
 nlinear wave systems. Our result is the wave analog of Lanford's theorem o
 n the derivation of the Boltzmann kinetic equation from particle systems\,
  where in both cases one takes the thermodynamic limit as the size of the 
 system diverges to infinity\, and as the interaction strength of waves or 
 radius of particles vanishes to 0\, according to some specified scaling la
 w. This is the first result of its kind for any nonlinear wave system.\n
LOCATION:https://researchseminars.org/talk/IMS/81/
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