A deterministic counterexample for high dimensional 𝐿²𝐿^{∞} Strichartz estimates for the Wave equation

Abstract

In this note we discuss the question of homogeneous L 2 L ∞ L^2 L^{\infty } Strichartz estimates for the Wave equation in dimensions n ≥ 4 n \geq 4 raised by Fang and Wang and recently shown to fail by Guo, Li, Nakanishi and Yan using probability theory. We record a deterministic example for disproving this estimate.