On Strichartz estimates and optimal blowup stability of supercritical wave equations

2024/11/24 by David Wallauch, Wallauch, David
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2411.15939

openalex publication_date 2024/11/24 · openalex created_date 2024/12/04 · openalex updated_date 2026/07/28

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≥ 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.

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