A note on certain scenarios of Type II blowups of suitable weak solutions to the Navier-Stokes equations

TL;DR

This paper investigates potential Type II blowups in solutions to the Navier-Stokes equations and demonstrates conditions under which such blowups cannot occur, implying regularity of solutions.

Contribution

It introduces new regularity results by ruling out certain Type II blowup scenarios using Euler scaling and Liouville theorems.

Findings

Certain Type II blowups are impossible under specific assumptions

Regularity results follow from the non-occurrence of these blowups

Uses Euler scaling and Liouville theorems for ancient solutions

Abstract

In the note, various scenarios of potential Type II blowups of suitable weak solutions to the Navier-Stokes equations are studied. It is shown, that under some assumptions, such type of blowups cannot happen. In this case, corresponding statements may be interpreted as regularity results. Their justification is based on a technique making use of a certain Euler scaling and Liouville type theorems for ancient solutions to the Euler system.