Communications in Mathematical Physics

, Volume 94, Issue 1, pp 61–66

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

  • J. T. Beale
  • T. Kato
  • A. Majda
Article

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.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • J. T. Beale
    • 1
  • T. Kato
    • 2
  • A. Majda
    • 2
  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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