Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations

Zihua Guo, Yuzhao Wang

Research output: Contribution to journalArticlepeer-review

61 Citations (Scopus)

Abstract

We prove some new Strichartz estimates for a class of dispersive equations with radial initial data. In particular, we obtain the full radial Strichartz estimates up to some endpoints for the Schrödinger equation. Using these estimates, we obtain some new results related to nonlinear problems, including small data scattering and large data LWP for the nonlinear Schrödinger and wave equations with radial critical initial data and the well-posedness theory for the fractional order Schrödinger equation in the radial case.
Original languageEnglish
Pages (from-to)1–38
JournalJournal d'Analyse Mathématique
Volume124
Issue number1
DOIs
Publication statusPublished - Oct 2014

Keywords

  • Dispersive Equation
  • Nonlinear Wave Equation
  • Critical Regularity
  • Strichartz Estimate
  • Radial Case

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