Global large solutions for the Navier-Stokes equations with the Coriolis force

TL;DR

This paper constructs global large solutions to the 3D Navier-Stokes equations with Coriolis force in critical Fourier-Besov spaces, allowing arbitrarily large initial data in these spaces.

Contribution

It introduces a method to obtain global solutions with large initial data in critical Fourier-Besov spaces for Navier-Stokes with Coriolis force.

Findings

Existence of global solutions for arbitrarily large initial data.

Solutions constructed in critical Fourier-Besov spaces.

Applicable to three-dimensional Navier-Stokes equations with Coriolis force.

Abstract

In this paper, we construct a class of global large solution to the three-dimensional Navier-Stokes equations with the Coriolis force in critical Fourier-Besov space $\dot{FB}^{2-\frac{3}{p}}_{p,r}(\mathbb{R}^3)$. In fact, our choice of special initial data $u_0$ can be arbitrarily large in $\dot{FB}^{s}_{p,r}(\mathbb{R}^3)$ for any $s\in\mathbb{R}$ and $1\leq p,r\leq \infty$.