Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations

Peter Constantin, Igor Kukavica, Vlad Vicol

Research output: Contribution to journalArticle

Abstract

We consider the incompressible Euler equations on Rd or Td, where d∈{2,3}. We prove that: (a) In Lagrangian coordinates the equations are locally well-posed in spaces with fixed real-analyticity radius (more generally, a fixed Gevrey-class radius). (b) In Lagrangian coordinates the equations are locally well-posed in highly anisotropic spaces, e.g. Gevrey-class regularity in the label a1 and Sobolev regularity in the labels a2,…,ad. (c) In Eulerian coordinates both results (a) and (b) above are false.

Original languageEnglish (US)
Pages (from-to)1569-1588
Number of pages20
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume33
Issue number6
DOIs
StatePublished - Nov 1 2016

Keywords

  • Analyticity
  • Euler equations
  • Gevrey class
  • Lagrangian and Eulerian coordinates

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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