Removing discretely self-similar singularities for the 3D Navier-Stokes equations

TL;DR

This paper investigates discretely self-similar blow-up solutions of the 3D Navier-Stokes equations, proving that such solutions have only one point singularity at blow-up time and removing the singularity when the scaling parameter is close to 1.

Contribution

The paper demonstrates the uniqueness of point singularities in discretely self-similar blow-up solutions and removes singularities for scaling parameters near 1, advancing understanding of Navier-Stokes singularities.

Findings

Discretely self-similar solutions have only one point singularity at blow-up time.

Singularities can be removed when the scaling parameter is close to 1.

Provides conditions under which blow-up solutions are regularized.

Abstract

We study the scenario of discretely self-similar blow-up for Navier-Stokes equations. We prove that at the possible blow-up time such solutions only one point singularity. In case of the scaling parameter $ \lambda $ near $ 1$ we remove the singularity.