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SUMMARY:Decay of the Maxwell field on the Schwarzschild spacetime - Federi
 co Pasqualotto (CCA)
DTSTART:20160120T160000Z
DTEND:20160120T170000Z
UID:TALK63736@talks.cam.ac.uk
CONTACT:Mr. Cambyse Rouzé
DESCRIPTION:The wave equation\, Maxwell's equations\, and the linearized E
 instein's equations have been intensively studied in order to understand t
 he stability properties of "black hole" solutions to Einstein's equations.
  Results for Maxwell's equations on a black hole background were first obt
 ained by Blue (2007)\, with further recent developments by Andersson\, Bae
 ckdahl and Blue (2015).\nIn this talk I will present a different approach 
 to proving decay properties of the Maxwell field on the Schwarzschild spac
 etime.\nThe key ideas are: 1) find a quantity which satisfies a Regge-Whee
 ler Equation\, admitting good estimates. Motivation for this approach lies
  in forthcoming work by Dafermos\, Holzegel and Rodnianski on the lineariz
 ed Einstein equations. 2) From such quantity\, show that all the component
 s of the field may be estimated. A key role is played by the r^p estimates
  of Dafermos and Rodnianski\, i.e. energy estimates with a hierarchy of we
 ights in the r variable.\nI will finally point out how this approach is su
 itable for application to a nonlinear problem involving the Maxwell-Born-I
 nfeld equations.\n
LOCATION:MR14\, Centre for Mathematical Sciences
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