Correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations

@article{Sharma2016CorrespondenceBK,
  title={Correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations},
  author={Ati S. Sharma and Igor Mezi'c and Beverley J. McKeon},
  journal={arXiv: Fluid Dynamics},
  year={2016},
  volume={1},
  pages={032402}
}
The relationship between Koopman mode decomposition, resolvent mode decomposition, and exact invariant solutions of the Navier-Stokes equations is clarified. The correspondence rests upon the invariance of the system operators under symmetry operations such as spatial translation. The usual interpretation of the Koopman operator is generalized to permit combinations of such operations, in addition to translation in time. This invariance is related to the spectrum of a spatiotemporal Koopman… 

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