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SUMMARY:Invariant Gibbs measures for the defocusing NLS on the real line -
  Tadahiro Oh (Edinburgh)
DTSTART:20140526T140000Z
DTEND:20140526T150000Z
UID:TALK49734@talks.cam.ac.uk
CONTACT:25129
DESCRIPTION:In 1994\, Bourgain constructed invariant Gibbs measures for NL
 S on the circle.  Then\, in 2000\, he considered the limit of these invari
 ant statistics\, by taking larger and lager periods\, and constructed uniq
 ue solutions for the defocusing (sub-)cubic NLS on the real line.  His res
 ult\, however\, focuses on the construction of solutions and does not disc
 uss the limiting Gibbs measures on the real line or their invariance.\n\nI
 n this talk\, we construct Gibbs measures for the defocusing NLS on the re
 al line as a stationary diffusion process in x.  Then\, we show that these
  Gibbs measures are invariant for the defocusing (sub-)quintic NLS on the 
 real line.  We also discuss the limit Gibbs measures for the Dirichlet bou
 ndary value problem on the real line as well as the half line\, allowing u
 s to construct new rough solutions in these settings.\n\nThis is a joint w
 ork with Jeremy Quastel (University of Toronto) and Philippe Sosoe (Harvar
 d University). 
LOCATION:CMS\, MR13
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