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SUMMARY: Global well-posedness and quasi-invariance of Gaussian measures f
 or fractional nonlinear Schrödinger equations - Justin Forlano (Edinburgh
 )
DTSTART:20231023T130000Z
DTEND:20231023T140000Z
UID:TALK207622@talks.cam.ac.uk
CONTACT:Dr Greg Taujanskas
DESCRIPTION:In this talk\, we discuss the long-time dynamics and statistic
 al properties of solutions to\nthe cubic fractional 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 quasi-invariant under the fl
 ow. In lower-dispersion settings\, the regularity of the initial data is b
 elow that amenable to the deterministic well-posedness theory. In our appr
 oach\, inspired by the seminal work by DiPerna-Lions (1989)\, we shift att
 ention from the flow of FNLS to controlling solutions to the infinite-dime
 nsional Liouville equation of the transported Gaussian measure. We establi
 sh suitable bounds in this setting\, which we then transfer back to the eq
 uation by adapting Bourgain’s invariant measure argument to quasi-invari
 ant measures.\nThis is a joint work with Leonardo Tolomeo (University of E
 dinburgh).
LOCATION:MR13
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