Well- and ill-posedness issues for energy supercritical waves

Slim Ibrahim, Mohamed Majdoub, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

We investigate the initial value problem for some energy supercritical semilinear wave equations. We establish local existence in suitable spaces with continuous flow. The proof uses the finite speed of propagation and a quantitative study of the associated ODE. It does not require any scaling invariance of the equation. We also obtain some ill-posedness and weak ill-posedness results.

Original languageEnglish (US)
Pages (from-to)341-367
Number of pages27
JournalAnalysis and PDE
Volume4
Issue number2
DOIs
StatePublished - 2011

Keywords

  • Finite speed of propagation
  • Ill-posedness
  • Nonlinear wave equation
  • Oscillating second order ODE
  • Well-posedness

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Well- and ill-posedness issues for energy supercritical waves'. Together they form a unique fingerprint.

  • Cite this