# Blow-up solutions to 3D Euler are hydrodynamically unstable

## TL;DR

This paper investigates the instability of solutions to the 3D Euler equations near potential singularities, highlighting the challenges in predicting blow-up through numerical methods.

## Contribution

It provides insights into the hydrodynamic instability associated with blow-up solutions and discusses the difficulties in numerical prediction of singularities.

## Key findings

- Solutions become unstable near blow-up time
- Numerical prediction of singularities is highly challenging
- Instability is linked to the propagation of regularity

## Abstract

We study the interaction between the stability, and the propagation of regularity, for solutions to the incompressible 3D Euler equation. It is still unknown whether a solution with smooth initial data can develop a singularity in finite time. This article explains why the prediction of such a blow-up, via direct numerical experiments, is so difficult. It is described how, in such a scenario, the solution becomes unstable as time approaches the blow-up time.