Global parametrices and dispersive estimates for variable coefficient wave equations

By Jason Metcalfe, D. Tataru. 2007

102 citations recorded by the source corpus.

In this article we consider variable coefficient time dependent wave equations in $${\mathbb {R} \times \mathbb {R}^n}$$ . Using phase space methods we construct outgoing parametrices and prove Strichartz type estimates globally in time. This is done in the context of C2 metrics which satisfy a weak asymptotic flatness condition at infinity.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fe872ab5eab4a4e303f45d1e1fb844087728aa76

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Concerning the wave equation on asymptotically Euclidean manifolds (2008, methodology): “The first seems to be that of Journ´e, Soer and Sogge [12] who proved global Strichartz estimates for Schr¨odinger operators with potential using local energy estimates (local smoothing) for eit . Stalani and Tataru [32] extended this philosphy by considering more general perturbations of , and more”
Local decay of waves on asymptotically flat stationary space-times (2009, unknown): “CA 94720-3840”
Decay estimates for variable coefficient wave equations in exterior domains (2008, methodology): “These estimates can be proved using a positive commutator argument with a multiplier which is roughly of the form f(r)∂r when n ≥ 3 and are quite akin to the bounds found in, e.g., [16], [24], [9], [20], [7], and [23].”
Strichartz Estimates on Schwarzschild Black Hole Backgrounds (2008, background): “Then (4.55) follows after summation.”