Well-posed Self-Similarity in Incompressible Standard Flows

Abstract

This article reviews the properties of the self-similar solutions of the Navier-Stokes equation for incompressible fluids. Since any smooth solution can be embedded into a self-similar solution at the identity scale, it follows that under standard flow conditions, the initial solution will remain smooth for all time as long as the self-similar solution is selected to have certain isobaric weight.

Supplementary material added (to see the Supplementary material, click on "TeX Source"): ChatGPT-4.5 Deep Research evaluation of this article, containing the proposed solution to the Navier-Stokes Millennium Problem; Exhaustive list of possible objections and responses; ChatGPT-3.5 executive summary of this work as a proposed solution to the Navier-Stokes Millennium Problem