Global regularity of two dimensional inhomogeneous incompressible Navier-Stokes Equations with large data

TL;DR

This paper proves the global regularity of two-dimensional inhomogeneous incompressible Navier-Stokes equations with large initial data, assuming viscosity depends on density with a positive lower bound, using a partial regularity approach.

Contribution

It establishes the global regularity for large data in 2D inhomogeneous Navier-Stokes equations with density-dependent viscosity, extending previous results to large initial data.

Findings

Global regularity for large data established

Enhanced decay estimates used in the proof

Results apply away from vacuum regions

Abstract

For two dimensional inhomogeneous Navier-Stokes of incompressible flows, with the assumption that the viscosity depends on the density but with a positive lower bound, using a partial regularity approach, in particular some enhanced decay estimates, we establish the global in time regularity for large data away from vacuum.