Remarks on the breakdown of smooth solutions for the 3-D Euler equations

J. T. Beale, T. Kato, A. Majda

Research output: Contribution to journalArticle

Abstract

The authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3-D Euler equations. In other words, if a solution of the Euler equations is initially smooth and loses its regularity at some later time, then the maximum vorticity necessarily grows without bound as the critical time approaches; equivalently, if the vorticity remains bounded, a smooth solution persists.

Original languageEnglish (US)
Pages (from-to)61-66
Number of pages6
JournalCommunications In Mathematical Physics
Volume94
Issue number1
DOIs
StatePublished - Mar 1984

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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