Remarks on the breakdown of smooth solutions for the 3- D Euler equations
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.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- March 1984
- DOI:
- 10.1007/BF01212349
- Bibcode:
- 1984CMaPh..94...61B