Dispersive estimate for the wave equation with the inverse-square potential

Fabrice Planchon, John G. Stalker, A. Shadi Tahvildar-Zadeh

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

We prove that spherically symmetric solutions of the Cauchy problem for the linear wave equation with the inverse-square potential satisfy a modified dispersive inequality that bounds the L norm of the solution in terms of certain Besov norms of the data, with a factor that decays in t for positive potentials. When the potential is negative we show that the decay is split between t and r, and the estimate blows up at r = 0. We also provide a counterexample showing that the use of Besov norms in dispersive inequalities for the wave equation are in general unavoidable.

Original languageEnglish (US)
Pages (from-to)1387-1400
Number of pages14
JournalDiscrete and Continuous Dynamical Systems
Volume9
Issue number6
DOIs
StatePublished - Nov 2003

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Dispersive estimates
  • Inverse-square potential
  • Time decay
  • Wave equation

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