Angular Regularity and Strichartz Estimates for the Wave Equation

TL;DR

This paper establishes sharp linear and bilinear Strichartz estimates for wave equations on Minkowski space, leveraging angular regularity of initial data to significantly expand the range of admissible exponents.

Contribution

It introduces a novel approach using angular regularity to improve Strichartz estimates for wave equations, with two different proofs provided.

Findings

Enhanced range of (q,r) exponents for wave equations

Sharp linear and bilinear Strichartz estimates

Angular regularity improves dispersive inequality bounds

Abstract

We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular momentum operators. In this setting, the range of (q,r) exponents vastly improves over what is available for the wave equations based on translation invariant derivatives of the initial data and the dispersive inequality. Two proofs of this result are given.