BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:A priori estimates in the energy space for the Che
rn-Simons-Schrödinger system - Zhuo Min "\;Har
old"\; Lim (University of Cambridge)
DTSTART;TZID=Europe/London:20151125T160000
DTEND;TZID=Europe/London:20151125T170000
UID:TALK61846AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61846
DESCRIPTION:The Chern-Simons-Schrödinger system is a gauge-cov
ariant version of the cubic nonlinear Schrödinger
equation in two space dimensions. It describes the
effective dynamics of a large system of nonrelati
vistic charged quantum particles in the plane\, in
teracting with each other and with a self-generate
d electromagnetic field. In this talk\, I will pre
sent some recent work towards establishing well-po
sedness in the energy space H^1^ for this system.
At this regularity\, energy methods alone are insu
fficient for proving the required a priori estimat
es\, and one has to exploit the dispersive nature
of the solutions. A major difficulty in doing so i
s the presence of a nonlinearity involving a deriv
ative\, a part of which is not amenable to a pertu
rbative treatment and has to be absorbed into the
principal operator. The methods used include Littl
ewood-Paley theory\, Bony's paraproduct decomposit
ions and the U^p^ and V^p^ spaces introduced by H.
Koch and D. Tataru in the context of nonlinear di
spersive equations. I will give a gentle\, but nec
essarily brisk\, overview of these techniques.
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:Adam Kashlak
END:VEVENT
END:VCALENDAR