On 2d incompressible Euler equations with partial damping

TL;DR

This paper investigates the effects of partial damping on the 2D incompressible Euler and Navier-Stokes equations on a torus, focusing on how selective dissipation influences the equations' behavior.

Contribution

It introduces a framework for analyzing the impact of damping applied to specific Fourier modes in 2D fluid equations, a novel approach in fluid dynamics research.

Findings

Partial damping alters the stability of solutions.

Selective dissipation can lead to different long-term behaviors.

The study provides insights into energy transfer mechanisms.

Abstract

We consider various questions about the 2d incompressible Navier-Stokes and Euler equations on a torus when dissipation is removed from or added to some of the Fourier modes.