Boundary De Giorgi-Ladyzhenskaya classes and their application to regularity of swirl of Navier-Stokes

TL;DR

This paper presents an embedding theorem for boundary DeGiorgi-Ladyzhenskaya classes into Hölder spaces, and applies this to analyze the regularity of swirl in Navier-Stokes equations.

Contribution

It introduces a new embedding theorem for boundary parabolic classes and applies it to establish regularity results for Navier-Stokes swirl.

Findings

Embedding theorem for boundary DeGiorgi-Ladyzhenskaya classes into Hölder spaces.

Application of the theorem to regularity of Navier-Stokes swirl.

Enhanced understanding of boundary regularity in parabolic PDEs.

Abstract

The embeddings theorem of space-boundary-type DeGiorgi-Ladyzhenskaya parabolic classes into Holder spaces is presented, which is useful for regularity considerations for parabolic boundary value problems. Additionaly, the application of this theory to Navier-Stokes-s swirl is presented.