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SUMMARY:Global well-posedness and quasi-invariance of Gaussian measures fo
 r fractional nonlinear Schrödinger equations
DTSTART:20231115T160000
DTEND:20231115T171500
DTSTAMP:20260917T084022Z
UID:7939ee38b81ef476772c0f83858b8a30e6edfba7a5096e5031b7192c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Justin Forlano (Edinburgh)\nIn this talk\, we discuss the long
 -time dynamics and statistical properties of solutions to the cubic fracti
 onal nonlinear Schrödinger equation (FNLS) on the one-dimensional torus\,
  with Gaussian initial data of negative regularity. We prove that FNLS is 
 almost surely globally well-posed and the associated Gaussian measure is q
 uasi-invariant under the flow. In lower-dispersion settings\, the regulari
 ty of the initial data is below that amenable to the deterministic well-po
 sedness theory. In our approach\, inspired by the seminal work by DiPerna-
 Lions (1989)\, we shift attention from the flow of FNLS to controlling sol
 utions to the infinite-dimensional Liouville equation of the transported G
 aussian measure. We establish suitable bounds in this setting\, which we t
 hen transfer back to the equation by adapting Bourgain’s invariant measu
 re argument to quasi-invariant measures.\n\nThis is a joint work with Leon
 ardo Tolomeo (University of Edinburgh).
LOCATION:Bernoulli center https://maps.app.goo.gl/LGa7ei1hQkCkkHN1A
STATUS:CANCELLED
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