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

Cristian Gavrus

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

Analysis of PDEs 2022-08-19 v1

Authors: Cristian Gavrus

Abstract

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.

Keywords

strichartz estimates

Cite

@article{arxiv.2208.08822,
  title  = {A deterministic counterexample for high dimensional $ L^2 L^{\infty} $ Strichartz estimates for the Wave equation},
  author = {Cristian Gavrus},
  journal= {arXiv preprint arXiv:2208.08822},
  year   = {2022}
}

Comments

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

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