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SUMMARY:On the well-posedness of the derivative nonlinear Schr\\"odinger e
 quation
DTSTART;TZID=America/Los_Angeles:20210422T090000
DTEND;TZID=America/Los_Angeles:20210422T095500
DTSTAMP:20241125T140624Z
UID:Analysis Seminar@Thu Apr 22 09:00:00 2021@main.oscweb.caltech.edu
CATEGORIES:
DESCRIPTION:Maria Ntekoume\, Department of Mathematics\, Rice University\n
 We consider the derivative nonlinear Schr \\&quot\;odinger equation in one
  space dimension\, posed both on the line and on the circle. This model is
  known to be completely integrable and $L^2$-critical with respect to scal
 ing. However\, not much is known regarding the well-posendess of the equat
 ion below $H^{\\frac 12}$. In this talk we prove that this problem is glob
 ally well-posed for initial data in the Sobolev spaces $H^s$ for $\\frac 1
  6\\leq s&lt\;\\frac 12$ under some restriction on the $L^2$ norm. The key
  ingredient in our argument is proving that ensembles of orbits with $L^2$
 -equicontinuous initial data remain equicontinuous under evolution. This i
 s joint work with Rowan Killip and Monica Visan.
LOCATION:Online Event
URL:https://www.caltech.edu/campus-life-events/calendar/analysis-seminar-9
 0029
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