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Singularities of Euler Flow? Not Out of the Blue!

โœ Scribed by U. Frisch; T. Matsumoto; J. Bec

Book ID
111568446
Publisher
Springer
Year
2003
Tongue
English
Weight
788 KB
Volume
113
Category
Article
ISSN
0022-4715

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This paper is about the problem of determining whether singularities can develop from analytic initial conditions in the Euler flow of three-dimensional hydrodynamics. The evidence is supplied by previous numerical simulations. To provide a guide for interpreting this numerical output, a theory base

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Self-similar solutions are considered to the incompressible Euler equations in R 3, where the similarity variable is defined as ~ = x/(T -t) f~ E R a, ~ \_ 0. It is shown that the scaling exponent is bounded above: 3 \_< 1. Requiring [[ui[ยฃu < oa and allowing more than one length scale, it is found/