On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations

TL;DR

This paper develops new a priori estimates for the 3D Euler, 3D Navier-Stokes, and 2D quasi-geostrophic equations using similarity transform methods, advancing understanding of these fundamental fluid dynamics models.

Contribution

It introduces a novel approach employing similarity transforms to derive a priori estimates for key fluid equations, which was not previously explored.

Findings

New a priori estimates for Euler, Navier-Stokes, and quasi-geostrophic equations

Method based on similarity transforms offers a fresh analytical tool

Potential implications for understanding solution regularity and blow-up

Abstract

We prove new \emph{a priori} estimates for the 3D Euler, the 3D Navier-Stokes and the 2D quasi-geostrophic equations by the method of similarity transforms.