Forward self-similar solutions to the 2D Navier--Stokes equations

TL;DR

This paper constructs self-similar solutions to the 2D Navier--Stokes equations from large initial data and provides numerical evidence suggesting these solutions may not be unique.

Contribution

It introduces a method to construct self-similar solutions from large initial data and explores their potential non-uniqueness through numerical analysis.

Findings

Existence of self-similar solutions from large initial data

Numerical evidence indicating possible non-uniqueness of solutions

Extension of solution classes for 2D Navier--Stokes equations

Abstract

We construct self-similar solutions to the 2D Navier--Stokes equations evolving from arbitrarily large $-1$--homogeneous initial data and present numerical evidence for their non-uniqueness.