# On the 3D Euler equations with Coriolis force in borderline Besov spaces

## TL;DR

This paper proves long-time existence and uniqueness of solutions for the 3D Euler equations with Coriolis force in borderline Besov spaces, especially under high rotation speeds, extending previous regularity results.

## Contribution

It introduces a broader class of initial data and establishes uniform estimates and a blow-up criterion for the equations in borderline Besov spaces.

## Key findings

- Long-time solvability for high rotation speeds
- Uniform estimates independent of rotation speed
- A blow-up criterion of BKM type

## Abstract

We consider the 3D Euler equations with Coriolis force (EC) in the whole space. We show long-time solvability in Besov spaces for high speed of rotation $\Omega $ and arbitrary initial data. For that, we obtain $\Omega$-uniform estimates and a blow-up criterion of BKM type in our framework. Our initial data class is larger than previous ones considered for (EC) and covers borderline cases of the regularity. The uniqueness of solutions is also discussed.