A deterministic counterexample for high dimensional $L^2{L}^{\infty }$ Strichartz estimates for the Wave equation

Abstract

In this note we discuss the question of homogeneous $L^2{L}^{\infty }$ Strichartz estimates for the Wave equation in dimensions $n\ge 4$ 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.

Published in "Proceedings of the Conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs" by the AMS in the Contemporary Mathematics (CONM) book series. 2021