On Strichartz estimates and optimal blowup stability of supercritical wave equations

TL;DR

This paper develops Strichartz estimates for radial wave equations with potentials across multiple dimensions, enabling optimal blowup stability analysis for supercritical nonlinear wave equations, including the quintic case.

Contribution

It introduces a unified framework of Strichartz estimates involving derivatives for supercritical wave equations in all dimensions d≥3, extending stability results.

Findings

Established Strichartz estimates for radial wave equations with potentials.

Derived optimal blowup stability results for supercritical nonlinear wave equations.

Applied results to the quintic nonlinear wave equation.

Abstract

We establish Strichartz estimates, including estimates involving spatial derivatives, for radial wave equations with potentials in similarity variables. This is accomplished for all spatial dimensions $d\geq 3$ and almost all regularities above energy and below the threshold $\frac d2$. These estimates provide a unified framework that allows one to derive optimal blowup stability result for a wide range of energy supercritical nonlinear wave equations. To showcase their usefulness, an optimal blowup stability result for the quintic nonlinear wave equation is also obtained.