Scattering for the Equivariant U(1) Problem

Abstract

Extending our previous works on the Cauchy problem for the $2+1$ equivariant Einstein-wave map system, we prove that the linear part dominates the nonlinear part of the wave maps equation coupled to the full set of the Einstein equations, for small data. A key ingredient in the proof is a nonlinear Morawetz estimate for the fully coupled equivariant Einstein-wave maps. The $2+1$ dimensional Einstein-wave map system occurs naturally in the U(1) symmetric $3+1$ dimensional vacuum Einstein equations of general relativity.

Published in Ann. Henri Poincaré (2024)

References in corpus (1)

• On the asymptotic behavior of solutions to Einstein's vacuum equations in wave coordinates