Self-similar solutions are considered to the incompressible Euler equations in , where the similarity variable is defined as , β ≥ 0. It is shown that the scaling exponent is bounded above: β ≤ 1. Requiring |u| 2 < ∞ and allowing more than one length scal

Introducing the concept of extremal subset to solve one open problem raised in [1]: find the conditions for a lower and upper bounds version of a variational inequality. A few applications are given.