Math @ Duke

Publications [#243340] of J. Thomas Beale
Papers Published
 Beale, JT; Kato, T; Majda, A, Remarks on the breakdown of smooth solutions for the 3D Euler equations,
Communications in Mathematical Physics, vol. 94 no. 1
(1984),
pp. 6166, ISSN 00103616 [doi]
(last updated on 2017/12/14)
Abstract: The authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3D 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 SpringerVerlag.


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