Regularity criteria of weak solutions to NSE in some bounded domains involving the pressure

TL;DR

This paper provides a new estimate for the pressure in bounded domains with slip boundary conditions, aiding in understanding the regularity of weak solutions to the Navier-Stokes equations.

Contribution

It introduces an elegant proof of pressure estimates and applies them to establish conditional regularity of weak solutions in specific bounded domains.

Findings

Pressure estimate in bounded domains derived

Application to conditional regularity of weak solutions

Enhanced understanding of boundary effects on Navier-Stokes solutions

Abstract

We present a short and elegant proof of an estimate for the pressure in terms of the velocity and external data in bounded domains under the slip and Navier boundary conditions. We also show an application of this result for conditional regularity of weak solutions to the Navier-Stokes equations.