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arXiv · 1805.01180

On the boundary Strichartz estimates for wave and Schr\"odinger equations

Zihua Guo·Ji Li·Kenji Nakanishi·Lixin Yan
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Abstract

We consider the $L_t^2L_x^r$ estimates for the solutions to the wave and Schr\"odinger equations in high dimensions. For the homogeneous estimates, we show $L_t^2L_x^\infty$ estimates fail at the critical regularity in high dimensions by using stable L\'evy process in $\R^d$. Moreover, we show that some spherically averaged $L_t^2L_x^\infty$ estimate holds at the critical regularity. As a by-product we obtain Strichartz estimates with angular smoothing effect. For the inhomogeneous estimates, we prove double $L_t^2$-type estimates.

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Zihua Guo, Ji Li, Kenji Nakanishi, Lixin Yan. 2018-05-03. On the boundary Strichartz estimates for wave and Schr\"odinger equations. https://arxiv.org/abs/1805.01180

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