On the boundary Strichartz estimates for wave and Schrödinger equations

Zihua Guo, Ji Li, Kenji Nakanishi, Lixin Yan

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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

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