Global well‐posedness result for density‐dependent incompressible viscous fluid in with linearly growing initial velocity

In this paper, we consider the density‐dependent incompressible Navier–Stokes equations in with linearly growing initial velocity at infinity. We obtain a blow‐up criterion and global well‐posedness of the two‐dimensional system. It generalized the local well‐posedness results due to the recent work by the first and third authors to the global well‐posedness in . Copyright © 2012 John Wiley & Sons, Ltd.