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

Yucong Huang; Aram Karakhanyan

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arXiv · 2511.02579

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

Yucong Huang·Aram Karakhanyan

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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.

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Yucong Huang, Aram Karakhanyan. 2025-11-04. A Monotonicity formula for almost self-similar suitable weak solutions to the stationary Navier-Stokes equations in $\mathbb R^5$. https://arxiv.org/abs/2511.02579

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