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[Β£u < oa and allowing more than one length scale, it is found/
An invariant for the 3D Euler equations
β Scribed by X. He
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 209 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0893-9659
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β¦ Synopsis
Communicated by D. G. Crighton
Abstract--We prove that for an ideal incompressible fluid in the presence of a conservative body force, there exists a time invariant, a vector A ---(Jtl,.42,.A3). It is discussed that the invariance of Ai is probably linked to geometrical structures of Navier-Stokes turbulence. (~) 1999 Elsevier Science Ltd. All rights reserved.
π SIMILAR VOLUMES
The propagation of Ho¨lder regularity of the solutions to the 3D Euler equations is discussed. Our method is a special semi-linearization of the vorticity equation combined with the classical Schauder interior estimates.
A sufficient integral criterion for a blow-up solution of the Hopf equations (the Euler equations with zero pressure) is found. This criterion shows that a certain positive integral quantity blows up in a finite time under specific initial conditions. Blow up of this quantity means that solution of