BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Transport of Gaussian measures along the flow of the nonlinear Sch
 rödinger equation.
DTSTART:20251203T134000Z
DTEND:20251203T142000Z
DTSTAMP:20260506T093400Z
UID:indico-event-15502@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexis Knezevitch\n\nIn this talk\, we provide a mac
 roscopic description of the solutions to the nonlinear Schrödinger equati
 on defined on the circle. In our approach\, the initial data are random va
 riables distributed according to Gaussian laws\, and therefore generate ra
 ndom solutions as well. Our main objective is to study their distributions
 \, in particular by comparing them with the initial Gaussian laws.\nThe fi
 rst works on Hamiltonian PDEs with random initial data go back to Lebowitz
 \, Rose\, and Speer (1987)\, and were later revisited by Bourgain. In thes
 e works\, the initial data are distributed according to the Gibbs measure\
 , which can be interpreted as choosing initial data at equilibrium. These 
 studies show that this equilibrium is preserved over time\, meaning that t
 he law of the solutions (at each instant) remains the Gibbs measure. In ot
 her words\, the flow preserves the Gibbs measure.\nHere\, we consider Gaus
 sian initial data\, which can now be interpreted as choosing them out of e
 quilibrium. We will see (under certain assumptions) that the laws of the s
 olutions are no longer identical\, but are in fact absolutely continuous w
 ith respect to the initial Gaussian laws. In other words\, the flow transp
 orts Gaussian measures into measures that are absolutely continuous with r
 espect to them. This is a qualitative result about the flow\, but quantita
 tive information on the Radon–Nikodym derivatives in turn yields more pr
 ecise properties of the solutions. This phenomenon\, called quasi-invaria
 nce\, was introduced by Nikolay Tzvetkov in 2015.\n\nhttps://indico.math.c
 nrs.fr/event/15502/
LOCATION:Fokko (ICJ)
URL:https://indico.math.cnrs.fr/event/15502/
END:VEVENT
END:VCALENDAR