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SUMMARY:Global well-posedness and quasi-invariance of Gaussian measures fo
r fractional nonlinear Schrödinger equations
DTSTART;VALUE=DATE-TIME:20240221T160000
DTEND;VALUE=DATE-TIME:20240221T170000
DTSTAMP;VALUE=DATE-TIME:20240422T020912Z
UID:b100635e510fd6609fd5e4ff38eab8ce7164f168b252e3a988e9d4f6
CATEGORIES:Conferences - Seminars
DESCRIPTION:Justin Forlano (Edinburgh)\nIn this talk\, we discuss the long
-time dynamics and statistical properties of solutions to\nthe cubic fract
ional 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 flow. In lower-dispersion settings\, the regular
ity of the initial data is below that amenable to the deterministic well-p
osedness theory. In our approach\, inspired by the seminal work by DiPerna
-Lions (1989)\, we shift attention from the flow of FNLS to controlling so
lutions to the infinite-dimensional Liouville equation of the transported
Gaussian measure. We establish suitable bounds in this setting\, which we
then transfer back to the equation by adapting Bourgain’s invariant meas
ure argument to quasi-invariant measures.\nThis is a joint work with Leona
rdo Tolomeo (University of Edinburgh).
LOCATION:Bernoulli center https://maps.app.goo.gl/LGa7ei1hQkCkkHN1A
STATUS:CONFIRMED
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