Decay estimates for the wave equation in two dimensions

TL;DR

This paper derives decay and Strichartz estimates for the 2D linear wave equation with a critical potential, providing new insights into decay behavior without resonances or eigenvalues at the spectrum edge, and explores simple nonlinear applications.

Contribution

It introduces decay and Strichartz estimates for the 2D wave equation with a near-critical potential, under resonance-free conditions, advancing understanding of wave decay in this setting.

Findings

Established Strichartz estimates in 2D with critical potential

Proved pointwise and weighted decay estimates

Applied results to simple nonlinear problems

Abstract

We establish Strichartz estimates (both reversed and some direct ones), pointwise decay estimates, and weighted decay estimates for the linear wave equation in dimension two with an almost scaling-critical potential, in the case when there is no resonance or eigenvalue at the edge of the spectrum. We also prove some simple nonlinear applications.