A Monotonicity formula for almost self-similar suitable weak solutions to the stationary Navier-Stokes equations in $\mathbb R^5$
Analysis of PDEs
2025-11-05 v1
Abstract
In this paper we show that a suitable weak solution to the stationary Navier-Stokes system in , 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 , and a projection theorem.
Keywords
Cite
@article{arxiv.2511.02579,
title = {A Monotonicity formula for almost self-similar suitable weak solutions to the stationary Navier-Stokes equations in $\mathbb R^5$},
author = {Yucong Huang and Aram Karakhanyan},
journal= {arXiv preprint arXiv:2511.02579},
year = {2025}
}