Local $\varepsilon$-regularity criteria for the five dimensional stationary Navier-Stokes equations

TL;DR

This paper develops new epsilon-regularity criteria for stationary Navier-Stokes equations in five dimensions, improving previous regularity results by employing iteration, Campanato's method, and interpolation.

Contribution

It introduces refined epsilon-regularity criteria at one scale for 5D stationary Navier-Stokes solutions, extending prior regularity conditions.

Findings

Established epsilon-regularity criteria in 5D

Improved previous regularity results

Used iteration, Campanato's method, and interpolation

Abstract

In this paper, we establish $\varepsilon$-regularity criteria at one scale for suitable weak solutions to the five dimensional stationary incompressible Navier-Stokes equations in both the unit ball $B_1$ and the unit half ball $B_1^+$, respectively, which improve previous results in [J. Math. Fluid Mech., 6(2004), pp 78--101] and [Comm. Pure Appl. Math., 41(1988), pp 437--458]. The proofs of the main results are based on an iteration argument, Campanato's method, and interpolation techniques.