# Global large solution to the compressible Navier-Stokes equations in critical Besov space $\dot{B}^{-1}_{\infty,\infty}$

## TL;DR

This paper constructs a class of global solutions for the compressible Navier-Stokes equations in the whole space, even with initial data having arbitrarily large norm in the critical Besov space, expanding understanding of solution existence.

## Contribution

It introduces a method to obtain global solutions with large initial data in the critical Besov space for the compressible Navier-Stokes equations, which was previously unresolved.

## Key findings

- Existence of global solutions with large initial data.
- Initial data can have arbitrarily large $
orm{
abla u_0}_{ ext{Besov}}$ norm.
- Solutions exist for all time despite large initial norms.

## Abstract

In this paper, we construct a class of global large solution to the compressible Navier-Stokes equations in the whole space $\R^d$. Precisely speaking, our choice of special initial data whose $\dot{B}^{-1}_{\infty,\infty}$ norm can be arbitrarily large, namely, $||u_0||_{\dot{B}^{-1}_{\infty,\infty}}\gg 1$, allows to give rise to global-in-time solution to the compressible Navier-Stokes equations.