Sharp decay estimates for an anisotropic linear semigroup and applications to the surface quasi-geostrophic and inviscid Boussinesq systems

Tarek M. Elgindi, Klaus Widmayer

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

At the core of this article is an improved, sharp dispersive estimate for the anisotropic linear semigroup eR1t arising in both the study of the dispersive surface quasi-geostrophic (SQG) equation and the inviscid Boussinesq system. We combine the decay estimate with a blow-up criterion to show how dispersion leads to long-time existence of solutions to the dispersive SQG equation, improving the results obtained using hyperbolic methods. In the setting of the inviscid Boussinesq system it turns out that linearization around a specific stationary solution leads to the same linear semigroup, so that we can make use of analogous techniques to obtain stability of the stationary solution for an increased time span.

Original languageEnglish (US)
Pages (from-to)4672-4684
Number of pages13
JournalSIAM Journal on Mathematical Analysis
Volume47
Issue number6
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Dispersive surface quasi-geostrophic equation
  • Inviscid Boussinesq system
  • Stability

Fingerprint Dive into the research topics of 'Sharp decay estimates for an anisotropic linear semigroup and applications to the surface quasi-geostrophic and inviscid Boussinesq systems'. Together they form a unique fingerprint.

  • Cite this