Titlebook: Harmonic Analysis and Partial Differential Equations; Michael Ruzhansky,Jens Wirth Book 2022 The Editor(s) (if applicable) and The Author(

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The Wave Resolvent for Compactly Supported Perturbations of Minkowski Space,elementary proof of the essential self-adjointness of □. and of uniform microlocal estimates for the resolvent in this setting. This provides a model for studying Lorentzian spectral zeta functions which is particularly simple, yet sufficiently general for locally deriving Einstein equations from a

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,Smoothing Effect and Strichartz Estimates for Some Time-Degenerate Schr?dinger Equations,l show that time-weighted smoothing and Strichartz estimates hold true for the operators under consideration. Finally, by means of the aforementioned estimates, we will derive local well-posedness results for the suitable corresponding nonlinear initial value problem.

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On the Cauchy Problem for the Nonlinear Wave Equation with Damping and Potential, result in Georgiev et al. (J. Differ. Equ. 267(5):3271–3288, 2019) into two directions. One is to relax the condition which characterizes the behavior of the coefficient of the damping term at spatial infinity as in (6). The other is to treat the slowly decreasing initial data. The decaying rate of

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