Publications [#243340] of J. Thomas Beale
- Beale, JT; Kato, T; Majda, A, Remarks on the breakdown of smooth solutions for the 3-D Euler equations,
Communications in Mathematical Physics, vol. 94 no. 1
pp. 61-66, Springer Nature, ISSN 0010-3616 [doi]
(last updated on 2019/11/18)
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. © 1984 Springer-Verlag.