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PRODID:Mathematics Seminar Calendar
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UID:20180117T201145-7231@math.msu.edu
DTSTAMP:20180117T201145Z
SUMMARY:Probabilistic scattering for the 4D energy-critical defocusing nonlinear wave equation
DESCRIPTION:Speaker\: Jonas Lührmann\r\nWe consider the Cauchy problem for the energy-critical defocusing \r\nnonlinear wave equation in four space dimensions. It is known that for \r\ninitial data at energy regularity, the solutions exist globally in time \r\nand scatter to free waves. However, the problem is ill-posed for initial \r\ndata at super-critical regularity, i.e. for regularities below the \r\nenergy regularity.\r\nIn this talk we study the super-critical data regime for this Cauchy \r\nproblem from a probabilistic point of view, using a randomization \r\nprocedure that is based on a unit-scale decomposition of frequency \r\nspace. We will present an almost sure global existence and scattering \r\nresult for randomized radially symmetric initial data of super-critical \r\nregularity. This is the first almost sure scattering result for an \r\nenergy-critical dispersive or hyperbolic equation for scaling \r\nsuper-critical initial data.\r\nThe main novelties of our proof are the introduction of an approximate \r\nMorawetz estimate to the random data setting and new large deviation \r\nestimates for the free wave evolution of randomized radially symmetric data.\r\n\r\nThis is joint work with Ben Dodson and Dana Mendelson.
LOCATION:C304 Wells Hall
DTSTART:20180125T160000Z
DTEND:20180125T170000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=7231
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