# Self-similar solutions for dyadic models of the Euler equations

## TL;DR

This paper proves the existence of self-similar solutions that follow Kolmogorov's scaling law for generalized dyadic models of the Euler equations, using dynamical systems analysis.

## Contribution

It extends previous results by establishing self-similar solutions for a broader class of dyadic Euler models.

## Key findings

- Existence of self-similar solutions satisfying Kolmogorov's scaling.
- Application of dynamical systems analysis to prove solutions.
- Extension of prior results to generalized dyadic models.

## Abstract

We show existence of self-similar solutions satisfying Kolmogorov's scaling for generalized dyadic models of the Euler equations, extending a result of Barbato, Flandoli, and Morandin. The proof is based on the analysis of certain dynamical systems on the plane.