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SUMMARY:Probabilistic Cauchy theory for NLS on the sphere
DTSTART:20251117T130000Z
DTEND:20251117T140000Z
DTSTAMP:20260505T203400Z
UID:indico-event-14500@indico.math.cnrs.fr
DESCRIPTION:Speakers: Chenmin Sun (LAMA - Université Paris-Est Créteil)\
 n\nIn this talk\, I will present some recent progress on the resolution of
  the cubic NLS on the sphere with random initial data. Our motivation is t
 o construct the dynamics on the support of the Gibbs measure\, as well as 
 the construction of solutions in the (deterministic) super-critical regime
 . For NLS on S^2\, we show that the Cauchy problem is globally well-posed 
 (in a suitable sense) with the initial data distributed according to the l
 aw of the Gibbs measure. For NLS on S^3 or B^3\, we can solve the cubic NL
 S under the radial symmetry\, but with regularity strictly below the typic
 al regularity of radial functions sampled from the Gibbs measure. In parti
 cular\, our three-dimensional result improves the result of Bourgain-Bulut
  for the same problem. This talk is based on a series joint works with Nic
 olas Burq\, Nicolas Camps and Nikolay Tzvetkov.\n\nhttps://indico.math.cnr
 s.fr/event/14500/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/14500/
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