Rotationally corrected scaling invariant solutions to the Navier-Stokes equations

TL;DR

This paper introduces new rotationally corrected self-similar solutions to the 3D Navier-Stokes equations, expanding the set of known solutions for large initial data in both whole and half spaces.

Contribution

It develops a novel class of solutions with rotational corrections to self-similar solutions, applicable to large initial data in $L^3_w$ spaces.

Findings

Constructed forward solutions for large initial data

Extended solutions to half spaces

Discussed backward solutions

Abstract

We introduce new classes of solutions to the three dimensional Navier-Stokes equations in the whole and half spaces that add rotational correction to self-similar and discretely self-similar solutions. We construct forward solutions in these new classes for arbitrarily large initial data in $L^3_w$ on the whole and half spaces. We also comment on the backward case.