The leading-order late-time asymptotic for linear waves on radially symmetric stationary perturbations of (2+1)-Minkowski space is proportional to u^{-1/2}v^{-1/2}.
Decay Estimates for the One-dimensional Wave Equation with an Inverse Power Potential
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Late-time tails for linear waves on radially symmetric stationary spacetimes of two space dimensions
The leading-order late-time asymptotic for linear waves on radially symmetric stationary perturbations of (2+1)-Minkowski space is proportional to u^{-1/2}v^{-1/2}.