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SUMMARY:Probabilistic global well-posedness of the energy-critical defocus
 ing nonlinear wave equation bellow the energy space - Oana Pocovnicu\, Her
 iot-Watt University
DTSTART:20160125T150000Z
DTEND:20160125T160000Z
UID:TALK63638@talks.cam.ac.uk
CONTACT:Amit Einav
DESCRIPTION:We consider the energy critical defocusing nonlinear wave equa
 tion (NLW) on R^d^ \, d=3\,4\,5. In the deterministic setting\, Christ\, C
 olliander\, and Tao showed that this equation is ill-posed below the energ
 y space H^1^ xL^2^.\nIn this talk we take a probabilistic approach. More p
 recisely\, we prove almost sure global existence and uniqueness for NLW wi
 th rough initial data below the energy space. The randomisation that we us
 e is naturally associated with the Wiener decomposition and with modulatio
 n spaces. The proof is based on probabilistic perturbation theory and on p
 robabilistic energy bounds.\nSecondly\, we prove analogous results in the 
 periodic setting\, for the energy critical NLW on T^d^\, d=3\,4\,5. The ma
 in 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 d
 iscuss how the above strategy also yields a conditional almost sure global
  well-posedness result below the scaling critical regularity\, for the def
 ocusing cubic nonlinear Schrödinger equation on Euclidean spaces.\nThis t
 alk is partially based on joint work with Tadahiro Oh and on joint work wi
 th Árpád Bényl and Tadahiro Oh.
LOCATION:CMS\, MR13
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