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.