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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:Probabilistic global well-posedness of the energy-
critical defocusing nonlinear wave equation bellow
the energy space - Oana Pocovnicu\, Heriot-Watt U
niversity
DTSTART;TZID=Europe/London:20160125T150000
DTEND;TZID=Europe/London:20160125T160000
UID:TALK63638AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/63638
DESCRIPTION:We consider the energy critical defocusing nonline
ar wave equation (NLW) on R^d^ \, d=3\,4\,5. In th
e deterministic setting\, Christ\, Colliander\, an
d Tao showed that this equation is ill-posed below
the energy space H^1^ xL^2^.\nIn this talk we tak
e a probabilistic approach. More precisely\, we pr
ove almost sure global existence and uniqueness fo
r NLW with rough initial data below the energy spa
ce. The randomisation that we use is naturally ass
ociated with the Wiener decomposition and with mod
ulation spaces. The proof is based on probabilisti
c perturbation theory and on probabilistic energy
bounds.\nSecondly\, we prove analogous results in
the periodic setting\, for the energy critical NLW
on T^d^\, d=3\,4\,5. The main idea is to use the
finite speed of propagation to reduce the problem
on T^d^ to a problem on Euclidean spaces. If time
allows\, we will briefly discuss how the above str
ategy also yields a conditional almost sure global
well-posedness result below the scaling critical
regularity\, for the defocusing cubic nonlinear Sc
hrödinger equation on Euclidean spaces.\nThis talk
is partially based on joint work with Tadahiro Oh
and on joint work with Árpád Bényl and Tadahiro O
h.
LOCATION:CMS\, MR13
CONTACT:Amit Einav
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