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SUMMARY:Andrea R. Nahmod (University of Massachusetts)
DTSTART:20201008T130000Z
DTEND:20201008T135000Z
DTSTAMP:20260423T035608Z
UID:IMS/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/63/">Inv
 ariant Gibbs measures and global strong solutions for periodic 2D nonlinea
 r Schrödinger equations.</a>\nby Andrea R. Nahmod (University of Massachu
 setts) as part of PDE seminar via Zoom\n\n\nAbstract\nIn this talk we will
  first give a quick background overview of Bourgain's approach to prove th
 e invariance of the Gibbs measure for the periodic cubic nonlinear Schrodi
 nger equation in 2D and of Gubinelli-Imkeller and Perkowski's para-control
 led calculus for parabolic stochastic equations. \nWe will then present ou
 r resolution of the long-standing problem of proving almost sure global we
 ll-posedness  (i.e. existence with uniqueness) for the periodic nonlinear 
 Schrödinger equation (NLS) in 2D on the support of the Gibbs measure\, fo
 r any (defocusing and renormalized) odd power nonlinearity. Consequently w
 e get the invariance of the Gibbs measure. This is achieved by a new metho
 d we call random averaging operators which precisely captures the intrinsi
 c randomness structure of the problematic high-low frequency interactions 
 at the heart of this NLS problem. \n\n\nThis is joint work with Yu Deng (U
 SC) and Haitian Yue (USC).\n
LOCATION:https://researchseminars.org/talk/IMS/63/
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