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CATEGORIES:Partial Differential Equations seminar
SUMMARY:About wave and SchrÃ¶dinger equations in the exteri
or of many strictly convex obstacles - David Lafon
taine\, University of Bath
DTSTART;TZID=Europe/London:20190218T150000
DTEND;TZID=Europe/London:20190218T160000
UID:TALK119044AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/119044
DESCRIPTION:In order to study the non-linear SchrÃ¶dinger and w
ave equations\, it is crucial to understand the de
cay of solutions of the associated linear equation
s. When a trapped trajectory exists\, a loss is un
avoidable for a first family of a-priori estimates
of the linear flow: the so-called smoothing estim
ates. In contrast\, we will show that in the exter
ior of many strictly convex obstacles\, the estima
tes of space-time norms of solutions\, known as St
richartz estimates\, hold with no loss with respec
t to the flat case\, as soon as the dynamic of the
trapped trajectories is sufficiently unstable. Fi
nally\, if time permits\, we will say a word about
the associated non-linear equations: if the geome
try does not induce too much concentration of ener
gy\, we expect that the solutions behave linearly
in large times.
LOCATION:CMS\, MR13
CONTACT:Ivan Moyano
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