On the Euler equations of incompressible fluids

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Abstract

Euler equations of incompressible fluids use and enrich many branches of mathematics, from integrable systems to geometric analysis. They present important open physical and mathematical problems. Examples include the stable statistical behavior of ill-posed free surface problems such as the Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The paper describes some of the open problems related to the incompressible Euler equations, with emphasis on the blowup problem, the inviscid limit and anomalous dissipation. Some of the recent results on the quasigeostrophic model are also mentioned.

Original languageEnglish (US)
Pages (from-to)603-621
Number of pages19
JournalBulletin of the American Mathematical Society
Volume44
Issue number4
DOIs
StatePublished - Oct 1 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Anomalous dissipation
  • Blowup
  • Euler
  • Free surface
  • Ill-posed
  • Quasigeostrophic equation
  • Turbulence
  • Vanishing viscosity

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