Self-similar solutions to the Navier-Stokes equations: a survey of recent results

TL;DR

This paper surveys recent developments in constructing forward self-similar solutions to the Navier-Stokes equations, including new extensions of existing results, providing a comprehensive overview of current research in this area.

Contribution

It offers a comprehensive survey of recent methods for constructing self-similar solutions and extends a key recent result in the field.

Findings

Compilation of various construction techniques for self-similar solutions

Extension of a recent significant result in the theory

Clarification of the role of self-similarity in Navier-Stokes solutions

Abstract

We survey the various constructions of forward self-similar solutions (and generalizations of self-similar solutions) to the Navier-Stokes equations. We also include and prove an extension of a recent result from [7].