2-D constrained Navier-Stokes equation and intermediate asymptotics

TL;DR

This paper introduces a modified 2-D Navier-Stokes equation that preserves key physical quantities to explore intermediate asymptotics, providing a formal analysis as a foundation for future rigorous studies.

Contribution

It proposes a new variant of the 2-D Navier-Stokes equation that maintains energy and momentum, aiming to better understand intermediate asymptotic behavior.

Findings

Formal analysis of the modified equation

Preservation of energy and momentum of inertia

Foundation for future rigorous study

Abstract

We introduce a modified version of the two-dimensional Navier-Stokes equation, preserving energy and momentum of inertia, which is motivated by the occurrence of different dissipation time scales and related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics. The analysis we present here is purely formal. A rigorous study of this equation will be done in a forthcoming paper.