Local boundary regularity for the Navier-Stokes equations in nonendpoint borderline Lorentz spaces

TL;DR

This paper establishes local boundary regularity results for certain distributional solutions of the Navier-Stokes equations within specific Lorentz spaces, advancing understanding of boundary behavior in fluid dynamics.

Contribution

It introduces new regularity results for Navier-Stokes solutions in nonendpoint Lorentz spaces, particularly near flat boundary parts.

Findings

Proves boundary regularity for solutions in $L_{ ext{infty}}L^{3,q}$ spaces.

Extends regularity theory to nonendpoint Lorentz spaces.

Provides conditions under which solutions are regular near flat boundary regions.

Abstract

We prove local regularity up to flat part of boundary, for certain classes of distributional solutions that are $L_{\infty}L^{3,q}$ with $q$ finite.