Strichartz estimates and local smoothing estimates for asymptotically flat Schr

By Jeremy Louis Marzuola, Jason Metcalfe, D. Tataru. 2007

114 citations recorded by the source corpus.

Abstract In this article we study global-in-time Strichartz estimates for the Schrodinger evolution corresponding to long-range perturbations of the Euclidean Laplacian. This is a natural continuation of a recent article [D. Tataru, Parametrices and dispersive estimates for Schrodinger operators with variable coefficients, Amer. J. Math. 130 (2008) 571–634] of the third author, where it is proved that local smoothing estimates imply Strichartz estimates. By [D. Tataru, Parametrices and dispersive estimates for Schrodinger operators with variable coefficients, Amer. J. Math. 130 (2008) 571–634] the local smoothing estimates are known to hold for small perturbations of the Laplacian. Here we consider the case of large perturbations in three increasingly favorable scenarios: (i) without non-trapping assumptions we prove estimates outside a compact set modulo a lower order spatially localized error term, (ii) with non-trapping assumptions we prove global estimates modulo a lower order spatially localized error term, and (iii) for time independent operators with no resonance or eigenvalue at the bottom of the spectrum we prove global estimates for the projection onto the continuous spectrum.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bae5177c77b095043ead736150baaf5acc4f1408

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Decay estimates for variable coefficient wave equations in exterior domains (2008, result): “This construction is reminiscent of those in [26], [ 10 ], and [13].”
Local decay of waves on asymptotically flat stationary space-times (2009, result): “9) is closely tied to a non-resonant spectral behavior at frequency 0 (see [30] for our similar results for Schrödinger evolutions).”