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

preprint2022arXivOpen access

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

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

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A deterministic counterexample for high dimensional L2L∞ L^2 L^{\infty} L2L∞ Strichartz estimates for the Wave equation

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