# Energy concentrations and Type I blow-up for the 3D Euler equations

## TL;DR

This paper proves that Type I blow-up, characterized by atomic energy concentrations, cannot occur in the 3D Euler equations and rules out discretely self-similar blow-up in energy-conserving scenarios.

## Contribution

It establishes the nonexistence of Type I blow-up and discretely self-similar blow-up solutions for the 3D Euler equations.

## Key findings

- Type I blow-up is excluded for 3D Euler equations.
- Discretely self-similar blow-up in energy conserving scale is impossible.
- Provides new insights into the regularity and blow-up behavior of Euler solutions.

## Abstract

We exclude Type I blow-up, which occurs in the form of atomic concentrations of the $L^2$ norm for the solution of the 3D incompressible Euler equations. As a corollary we prove nonexistence of discretely self-similar blow-up in the energy conserving scale.