# Boundary $\varepsilon$-regularity criteria for the 3D Navier-Stokes equations

## TL;DR

This paper develops boundary epsilon-regularity criteria for suitable weak solutions of the 3D Navier-Stokes equations near boundaries, extending interior regularity results and employing advanced iteration and interpolation methods.

## Contribution

It introduces new boundary epsilon-regularity criteria for the 3D Navier-Stokes equations, providing alternative proofs and extending previous interior regularity results to boundary cases.

## Key findings

- Established boundary epsilon-regularity criteria for weak solutions.
- Extended interior regularity results to boundary scenarios.
- Used iteration and interpolation techniques for proofs.

## Abstract

We establish several boundary $\varepsilon$-regularity criteria for suitable weak solutions for the 3D incompressible Navier-Stokes equations in a half cylinder with the Dirichlet boundary condition on the flat boundary. Our proofs are based on delicate iteration arguments and interpolation techniques. These results extend and provide alternative proofs for the earlier interior results by Vasseur [18], Choi-Vasseur [2], and Phuc-Guevara [6].