A Monotonicity formula for almost self-similar suitable weak solutions to the stationary Navier-Stokes equations in ${\mathbb{R}}^5$

Abstract

In this paper we show that a suitable weak solution to the stationary Navier-Stokes system in ${\mathbb{R}}^5$, cannot behave like a self-similar function of degree negative one if the lower limit of the local Reynolds number is finite. To prove the result we develop a method that uses a monotonicity formula approach, classification of homogenous solutions to the incompressible Euler equations in ${\mathbb{R}}^5$, and a projection theorem.