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The three-dimensional Euler equations: singular or non-singular?

J D Gibbon1, M Bustamante2 and R M Kerr2

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OPEN PROBLEM

One of the outstanding open questions in modern applied mathematics is whether solutions of the incompressible Euler equations develop a singularity in the vorticity field in a finite time. This paper briefly reviews some of the issues concerning this problem, together with some observations that may suggest that it may be more subtle than first thought.


PACS

47.10.A- Mathematical formulations

47.32.C- Vortex dynamics

MSC

76M23 Vortex methods

76Bxx Incompressible inviscid fluids

Subjects

Fluid dynamics

Mathematical physics

Dates

Issue 8 (August 2008)

Received 4 April 2008

Published 16 June 2008



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