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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Invariant Gibbs measures for the defocusing NLS on
the real line - Tadahiro Oh (Edinburgh)
DTSTART;TZID=Europe/London:20140526T150000
DTEND;TZID=Europe/London:20140526T160000
UID:TALK49734AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/49734
DESCRIPTION:In 1994\, Bourgain constructed invariant Gibbs mea
sures for NLS on the circle. Then\, in 2000\, he
considered the limit of these invariant statistics
\, by taking larger and lager periods\, and constr
ucted unique solutions for the defocusing (sub-)cu
bic NLS on the real line. His result\, however\,
focuses on the construction of solutions and does
not discuss the limiting Gibbs measures on the rea
l line or their invariance.\n\nIn this talk\, we c
onstruct Gibbs measures for the defocusing NLS on
the real 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 me
asures for the Dirichlet boundary value problem on
the real line as well as the half line\, allowing
us to construct new rough solutions in these sett
ings.\n\nThis is a joint work with Jeremy Quastel
(University of Toronto) and Philippe Sosoe (Harvar
d University).
LOCATION:CMS\, MR13
CONTACT:
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