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arXiv · 2204.01157

Scattering for the Equivariant U(1) Problem

Nishanth Gudapati
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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.

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Nishanth Gudapati. 2022-04-03. Scattering for the Equivariant U(1) Problem. https://doi.org/10.1007/s00023-024-01503-5

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