Global Well-Posedness for the 2-D Inhomogeneous Incompressible Navier-Stokes System with Large Initial Data in Critical Spaces

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.