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

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.