Long Time Stability for Solutions of a β-Plane Equation

Tarek M. Elgindi, Klaus Widmayer

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We prove stability for arbitrarily long times of the zero solution for the so-called β-plane equation, which describes the motion of a two-dimensional inviscid, ideal fluid under the influence of the Coriolis effect. The Coriolis force introduces a linear dispersive operator into the two-dimensional incompressible Euler equations, thus making this problem amenable to an analysis from the point of view of nonlinear dispersive equations. The dispersive operator, L1:(Formula presented.), exhibits good decay, but has numerous unfavorable properties, chief among which are its anisotropy and its behavior at small frequencies.

Original languageEnglish (US)
Pages (from-to)1425-1471
Number of pages47
JournalCommunications on Pure and Applied Mathematics
Volume70
Issue number8
DOIs
StatePublished - Aug 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Long Time Stability for Solutions of a β-Plane Equation'. Together they form a unique fingerprint.

  • Cite this