Communications in Mathematical Physics

, Volume 155, Issue 2, pp 277–294

On the blow-up of solutions of the 3-D Euler equations in a bounded domain

  • Andrew B. Ferrari
Article

DOI: 10.1007/BF02097394

Cite this article as:
Ferrari, A.B. Commun.Math. Phys. (1993) 155: 277. doi:10.1007/BF02097394

Abstract

It is shown that if [0,\(\hat T\)) is the maximal interval of existence of a smooth solutionu of the incompressible Euler equations in a bounded, simply connected domain Ω\( \subseteq\)R3, then\(\int_0^{\hat T} {\left| {\omega ( \cdot ,t)} \right|_{L^\infty (\Omega )} } dt = \infty\), where ω=∇×u is the vorticity. Crucial to this result is a special estimate proven in Ω of the maximum velocity gradient in terms of the maximum vorticity and a logarithmic term involving a higher norm of the vorticity.

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Andrew B. Ferrari
    • 1
  1. 1.Department of MathematicsDuke UniversityDurhamUSA