Refined Strichartz inequalities for the wave equation

TL;DR

This paper extends refined Strichartz inequalities from the Schrödinger equation to the wave equation, leading to improved fractal Strichartz bounds in higher dimensions.

Contribution

It introduces analogues of Schrödinger refined Strichartz inequalities for the wave equation, enhancing existing $L^2$ fractal inequalities in dimensions $d \, \geq \, 4$.

Findings

Improved $L^2$ fractal Strichartz inequalities for the wave equation in dimensions $d \geq 4$.

Established analogues of Schrödinger refined inequalities for the wave equation.

Enhanced understanding of wave equation behavior in higher-dimensional fractal settings.

Abstract

Some analogues of the Schr\"odinger refined Strichartz inequalities (Du, Guth, Li and Zhang) are obtained for the wave equation. These are used to improve the best known $L^2$ fractal Strichartz inequalities for the wave equation in dimensions $d \geq 4$.