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arXiv · 2411.15939

On Strichartz estimates and optimal blowup stability of supercritical wave equations

David Wallauch
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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.

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David Wallauch. 2024-11-24. On Strichartz estimates and optimal blowup stability of supercritical wave equations. https://arxiv.org/abs/2411.15939

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