Dispersive and Strichartz estimates for the three-dimensional wave equation with a scaling-critical class of potentials

The Anh Bui, Xuan Thinh Duong, Younghun Hong*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    We consider the three-dimensional linear wave equation perturbed by a potential V belonging to a scaling-critical class which is the closure of bounded, compactly supported functions with respect to the global Kato norm. Without any further smallness assumptions, we first prove the dispersive estimate for the solution of the wave equation. As a byproduct, we prove Strichartz estimates under a slightly stronger condition.

    Original languageEnglish
    Pages (from-to)2215-2246
    Number of pages32
    JournalJournal of Functional Analysis
    Volume271
    Issue number8
    DOIs
    Publication statusPublished - 15 Oct 2016

    Keywords

    • Besov space
    • Dispersive estimate
    • Kato potential
    • Wave equation

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