BEGIN:VCALENDAR
VERSION:2.0
PRODID:icalendar-ruby
CALSCALE:GREGORIAN
X-WR-CALNAME:PDE/Analysis Seminar
X-WR-TIMEZONE:Eastern Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20260711T180633Z
UID:tag:localist.com\,2008:EventInstance_3607275
DTSTART:20180508T200000Z
DTEND:20180508T210000Z
DESCRIPTION:Jonas Luehrmann (Johns Hopkins)\n\n"Probabilistic local well-po
 sedness and scattering for the 4D cubic NLS"\n\nAbstract:\n\nWe consider t
 he Cauchy problem for the defocusing cubic nonlinear Schrodinger equation 
 (NLS) in four space dimensions. It is known that for initial data at energ
 y regularity\, the solutions exist globally in time and scatter. However\,
  the problem is ill-posed for initial data at super-critical regularity\, 
 i.e. for regularities below the energy regularity. In this talk we study t
 he super-critical data regime for this Cauchy problem from a probabilistic
  point of view\, using a randomization procedure that is based on a unit-s
 cale decomposition of frequency space. In the first part of the talk we wi
 ll explain how the problem of establishing almost sure local existence for
  the cubic NLS for such random data has some features in common with provi
 ng local existence for a derivative NLS equation. Our method is inspired b
 y the local smoothing estimates and functional frameworks from the Schrodi
 nger maps literature. In the second part of the talk we will turn to the l
 ong-time dynamics of the solutions. We will present a conditional almost s
 ure scattering result and an\nalmost sure scattering result for randomized
  radial data.\n\nThis is joint work with Ben Dodson and Dana Mendelson.
LOCATION:2-135
SUMMARY:PDE/Analysis Seminar
URL;VALUE=URI:https://calendar.mit.edu/event/pdeanalysis_seminar_1714
CATEGORIES:Conferences/Seminars/Lectures
END:VEVENT
END:VCALENDAR