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DTSTART:20180325T030000
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DTSTART:20181028T020000
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DTSTAMP:20230327T173719Z
UID:59c8cedc499e9183981214@ist.ac.at
DTSTART:20180703T160000
DTEND:20180703T180000
DESCRIPTION:Speaker: Jonas Luehrmann\nhosted by Laszlo ErdÃ¶s\nAbstract: In
the classical well-posedness theory for nonlinear dispersive and hyperbol
ic equations the aim is to construct unique strong solutions for all initi
al data belonging to a certain function space such as the L^2-based Sobole
v spaces. However\, at low regularities ill-posedness phenomena usually te
nd to occur. In practice one is often interested in the typical behavior o
f solutions and may be content to neglect certain pathological behaviors l
eading to ill-posedness results. This concept may be formalized by conside
ring random initial data and by trying to construct in an almost sure mann
er strong local-in-time or even global-in-time solutions. Such an approach
sometimes allows to go beyond certain deterministic regularity thresholds
.I will begin this talk with a general introduction to the study of nonlin
ear dispersive and hyperbolic equations for random initial data. Afterward
s I will present an almost sure global existence and scattering result for
the 4D energy-critical nonlinear wave equation for scaling super-critical
random data in the radial case.This talk is based on joint works with Ben
Dodson and Dana Mendelson.
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Jonas Luehrmann: Random data Cauchy theory for nonlinear wave equat
ions
URL:https://talks-calendar.ista.ac.at/events/1288
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