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Showing content from https://link.springer.com/doi/10.1007/BF01205787 below:

Remarks on a paper by J. T. Beale, T. Kato, and A. Majda

We prove that the maximum norm of the deformation tensor controls the possible breakdown of smooth solutions for the 3-dimensional Euler equations. More precisely, the loss of regularity in a local smooth solution of the Euler equations implies the growth without bound of the deformation tensor as the critical time approaches; equivalently, if the deformation tensor remains bounded the existence of a smooth solution is guaranteed.

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1. Beale, J. T., Kato, T., Majda, A.: Remarks on the breakdown of smooth solutions for the 3-D Euler equations (preprint)

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1. Escuela de Fisica, Mathematicas, Fac, de Ciencias Universidad Central de Venezuela, Apartado 50.925, Caracas, Venezuela

   Gustavo Ponce

Communicated by L. Nirenberg

Ponce, G. Remarks on a paper by J. T. Beale, T. Kato, and A. Majda. Commun.Math. Phys. 98, 349–353 (1985). https://doi.org/10.1007/BF01205787

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• Received: 01 August 1983

• Issue Date: September 1985

• DOI: https://doi.org/10.1007/BF01205787

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