# Persistence of the solution to the Euler equations in the end-point critical Triebel-Lizorkin space $F^{d+1}_{1, \infty}(\mathbb{R}^d)$

## TL;DR

This paper investigates the persistence of solutions to the Euler equations for incompressible fluids within the critical Triebel-Lizorkin space at the endpoint, clarifying conditions for solution stability.

## Contribution

It provides new insights into the local persistence of solutions in the endpoint Triebel-Lizorkin space $F^{d+1}_{1, ext{infinity}}$, a critical function space for Euler equations.

## Key findings

- Solutions persist locally in the endpoint Triebel-Lizorkin space
- Clarifies conditions for solution stability at the critical endpoint
- Advances understanding of Euler equations in advanced function spaces

## Abstract

Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end-point Triebel-Lizorkin spaces $F^s_{1, \infty}(\mathbb{R}^d)$ with $s \geq d + 1$ is clarified.