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On Scattering for Small Data of \(\varvec{2 + 1}\)-Dimensional Equivariant Einstein-Wave Map System

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Abstract

We consider the Cauchy problem of \(2+1\) equivariant wave maps coupled to Einstein’s equations of general relativity and prove that two separate (nonlinear) subclasses of the system disperse to their corresponding linearized equations in the large. Global asymptotic behavior of \(2+1\) Einstein-wave map system is relevant because the system occurs naturally in \(3+1\) vacuum Einstein’s equations.

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Authors and Affiliations

  1. Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD, 21218, USA

    Benjamin Dodson

  2. Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, CT, 06511, USA

    Nishanth Gudapati

Authors
  1. Benjamin Dodson
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  2. Nishanth Gudapati
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Correspondence to Nishanth Gudapati.

Additional information

Communicated by James A. Isenberg.

(BD) is supported by NSF by grant no. DMS-1500424 and (NG) is supported by Deutsche Forschungsgemeinschaft (DFG) Postdoctoral Fellowship GU1513/1-1 to Yale University.

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Dodson, B., Gudapati, N. On Scattering for Small Data of \(\varvec{2 + 1}\)-Dimensional Equivariant Einstein-Wave Map System. Ann. Henri Poincaré 18, 3097–3142 (2017). https://doi.org/10.1007/s00023-017-0599-5

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  • DOI: https://doi.org/10.1007/s00023-017-0599-5

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