# Global well-posedness for the 2-D inhomogeneous incompressible Navier-Stokes system with large initial data in critical spaces

## TL;DR

This paper proves the global existence and uniqueness of solutions for the 2-D inhomogeneous incompressible Navier-Stokes equations with large initial data in critical Besov spaces, without smallness assumptions.

## Contribution

It establishes the first global well-posedness result for large initial data in critical spaces for this system, extending previous results that required small data.

## Key findings

- Global unique solvability without smallness condition
- Initial data in critical Besov space suffices for well-posedness
- Results apply to nearly energy space in 2-D

## Abstract

Without any smallness assumption, we prove the global unique solvability of the 2-D incompressible inhomogeneous Navier-Stokes equations with initial data in the critical Besov space, which is almost the energy space in the sense that they have the same scaling in terms of this 2-D system.