On the boundary Strichartz estimates for wave and Schrödinger equations

Zihua Guo*, Ji Li, Kenji Nakanishi, Lixin Yan

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    We consider the Lt 2Lx r estimates for the solutions to the wave and Schrödinger equations in high dimensions. For the homogeneous estimates, we show Lt 2Lx estimates fail at the critical regularity in high dimensions by using stable Lévy process in Rd. Moreover, we show that some spherically averaged Lt 2Lx 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 Lt 2-type estimates.

    Original languageEnglish
    Pages (from-to)5656-5675
    Number of pages20
    JournalJournal of Differential Equations
    Volume265
    Issue number11
    DOIs
    Publication statusPublished - 5 Dec 2018

    Keywords

    • Nonlinear Schrödinger equation
    • Nonlinear wave equation
    • Strichartz estimates

    Fingerprint Dive into the research topics of 'On the boundary Strichartz estimates for wave and Schrödinger equations'. Together they form a unique fingerprint.

    Cite this