Rescalings at possible singularities of Navier-Stokes equations in half space

TL;DR

This paper introduces the concept of mild bounded ancient solutions in a half space to analyze potential singularities in Navier-Stokes equations, aiming to understand blowup behavior under non-slip boundary conditions.

Contribution

It proposes a new class of solutions to study singularities in Navier-Stokes equations with boundary conditions, advancing the understanding of blowup phenomena.

Findings

Introduced mild bounded ancient solutions in half space

Provided insights into Type I blowups for Navier-Stokes

Enhanced understanding of boundary effects on singularities

Abstract

In the paper, we have introduced the notion of mild bounded ancient solutions to the Navier-Stokes equations in a half space. They play a certain role in understanding whether or not solutions to the initial boundary value problem for the Navier-Stokes system with non-slip boundary conditions have blowups of Type I.