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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:The global stability of the Minkowski spacetime so
lution to the Einstein-nonlinear electromagnetic s
ystem in wave coordinates - Jared Speck (Princeton
)
DTSTART;TZID=Europe/London:20110404T160000
DTEND;TZID=Europe/London:20110404T170000
UID:TALK30622AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/30622
DESCRIPTION:The Einstein-nonlinear electromagnetic system is a
coupling of the Einstein field equations of gener
al relativity to nonlinear electromagnetic field e
quations. In this talk\, I will discuss the family
of covariant electromagnetic models that satisfy
the following criteria: i) they are derivable from
a sufficiently regular Lagrangian\, ii) they redu
ce to the familiar Maxwell model in the weak-field
limit\, and iii) their corresponding energy-momen
tum tensors satisfy the dominant energy condition.
I will mention several specific electromagnetic m
odels that are of interest to researchers working
in the foundations of physics. I will then discuss
my main result\, which is a proof of the global n
onlinear stability of the 1 + 3 dimensional Minkow
ski spacetime solution to the coupled system. This
stability result is a consequence of a small-data
global existence result for a reduced system of e
quations that is equivalent to the original system
in a wave coordinate gauge. The analysis of the s
pacetime metric components is based on a framework
recently developed by Lindblad and Rodnianski\, w
hich allows one to derive suitable estimates for t
ensorial systems of quasilinear wave equations wit
h nonlinearities that satisfy the weak null condit
ion. The analysis of the electromagnetic fields\,
which satisfy quasilinear first-order equations\,
is based on an extension of a geometric energy-met
hod framework developed by Christodoulou\, togethe
r with a collection of pointwise decay estimates f
or the Faraday tensor that I develop. Throughout t
he analysis\, I work directly with the electromagn
etic fields\, thus avoiding the introduction of el
ectromagnetic potentials.
LOCATION:CMS\, MR13
CONTACT:Prof. Mihalis Dafermos
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