On the boundary Strichartz estimates for wave and Schrödinger equations

We consider the Lt2Lxr estimates for the solutions to the wave and Schrödinger equations in high dimensions. For the homogeneous estimates, we show Lt2Lx∞ estimates fail at the critical regularity in high dimensions by using stable Lévy process in Rd. Moreover, we show that some spherically averaged...

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Bibliographic Details
Published in:Journal of Differential Equations 2018-12, Vol.265 (11), p.5656-5675
Main Authors: Guo, Zihua, Li, Ji, Nakanishi, Kenji, Yan, Lixin
Format: Article
Language:English
Subjects:
Nonlinear Schrödinger equation
Nonlinear wave equation
Strichartz estimates
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Summary:We consider the Lt2Lxr estimates for the solutions to the wave and Schrödinger equations in high dimensions. For the homogeneous estimates, we show Lt2Lx∞ estimates fail at the critical regularity in high dimensions by using stable Lévy process in Rd. Moreover, we show that some spherically averaged Lt2Lx∞ 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 Lt2-type estimates.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2018.07.010