BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:The nonlinear stability of the Maxwell-Born-Infeld System - Jared 
 Speck (DPMMS)
DTSTART:20100517T150000Z
DTEND:20100517T160000Z
UID:TALK24861@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:The Maxwell-Born-Infeld (MBI) system is a nonlinear model of c
 lassical electromagnetism that was introduced in the 1930s. It is the uniq
 ue model that is derivable from an action principle and that satisfies 5 p
 hysically compelling postulates. In this talk\, I will use an electromagne
 tic gauge invariant framework to establish the existence of small-data glo
 bal solutions to the MBI system on the Minkowski space background in 1 + 3
  dimensions. The nonlinearities in the PDEs satisfy a version of the null 
 condition\, which means that they have special algebraic structure that pr
 ecludes the presence of the “worst possible combinations” of terms. As
  a consequence\, we are also able to show that the global solutions have e
 xactly the same decay properties as solutions to the linear Maxwell-Maxwel
 l system\, which were derived by Demetrios Christodoulou and Sergiu Klaine
 rman (1990). Our results complement the large-data blowup results for plan
 e-symmetric MBI solutions\, which were shown first by Yan Brenier (2002)\,
  and later by J. Speck (2008). As a byproduct of our analysis\, we also sh
 ow that the MBI system is hyperbolic in all field-strength regimes where t
 he equations are well-defined.
LOCATION:CMS\, MR13
END:VEVENT
END:VCALENDAR