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SUMMARY:Sharp decay for a family of solutions to the SU(2) Yang-Mills equa
 tions on a Schwarzschild black hole.
DTSTART:20251201T130000Z
DTEND:20251201T140000Z
DTSTAMP:20260505T203400Z
UID:indico-event-14444@indico.math.cnrs.fr
DESCRIPTION:Speakers: Pascal Millet (LAGA - Université Sorbonne Paris Nor
 d)\n\nThe purely magnetic ansatz yields a family of spherically symmetric 
 solutions to the SU(2) Yang-Mills equations parametrized by a single scala
 r function $W$. The equation on $W$ is a semilinear wave equation exhibiti
 ng rich dynamics while avoiding the algebraic complexity of the full Yang-
 Mills system. On the Schwarzschild spacetime\, previous results include gl
 obal existence\, existence of an infinite family of unstable stationary so
 lutions and stability of the trivial solutions $W =\\pm 1$. In this talk\,
  I will present a work in progress\, joint with Cécile Huneau\, adressing
  a conjecture of Bizoń-Chmaj-Rostworowski about the precise late-time asy
 mptotics for solutions initially close to $W=1$. This sharpens the decay r
 ate previously obtained by Ghanem-Häfner and provides a concrete example 
 of how the nonlinearity and its structure influence the decay rate of the 
 solution. In particular\, the decay rate for the nonlinear problem differs
  from that of the corresponding linearized problem.\n\nhttps://indico.math
 .cnrs.fr/event/14444/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/14444/
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