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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:The nonlinear stability of the Maxwell-Born-Infeld
System - Jared Speck (DPMMS)
DTSTART;TZID=Europe/London:20100517T160000
DTEND;TZID=Europe/London:20100517T170000
UID:TALK24861AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/24861
DESCRIPTION:The Maxwell-Born-Infeld (MBI) system is a nonlinea
r model of classical electromagnetism that was int
roduced in the 1930s. It is the unique model that
is derivable from an action principle and that sat
isfies 5 physically compelling postulates. In this
talk\, I will use an electromagnetic gauge invari
ant framework to establish the existence of small-
data global solutions to the MBI system on the Min
kowski space background in 1 + 3 dimensions. The n
onlinearities in the PDEs satisfy a version of the
null condition\, which means that they have speci
al algebraic structure that precludes the presence
of the “worst possible combinations” of terms. As
a consequence\, we are also able to show that the
global solutions have exactly the same decay prop
erties as solutions to the linear Maxwell-Maxwell
system\, which were derived by Demetrios Christodo
ulou and Sergiu Klainerman (1990). Our results com
plement the large-data blowup results for plane-sy
mmetric MBI solutions\, which were shown first by
Yan Brenier (2002)\, and later by J. Speck (2008).
As a byproduct of our analysis\, we also show tha
t the MBI system is hyperbolic in all field-streng
th regimes where the equations are well-defined.
LOCATION:CMS\, MR13
CONTACT:Prof. Mihalis Dafermos
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