# On some model equations of Euler and Navier-Stokes equations

## TL;DR

This paper introduces a 2D generalization of a model related to Euler equations, explores singular solutions, and discusses potential links to turbulence and Navier-Stokes singularities.

## Contribution

It presents a new 2D model extending Constantin-Lax-Majda, analyzing singular solutions and their implications for Euler and Navier-Stokes equations.

## Key findings

- Existence of singular solutions in the proposed model
- Potential connections between turbulence and Navier-Stokes singularities
- New model equations capturing aspects of fluid dynamics difficulties

## Abstract

We propose a two-dimensional generalization of Constantin-Lax-Majda model [2]. Some results about singular solutions are given. This model might be the first step toward the singular solutions of the Euler equations. Along the same line (vorticity formulation), we present some further model equations. They possibly models various aspects of difficulties related with the singular solutions of the Euler and Navier-Stokes equations. We also make some discussions on the possible connection between turbulence and the singular solutions of the Navier-Stokes equations.