English

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 R5\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 R5\mathbb R^5, 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}
}