The Leray problem for 2D inhomogeneous fluids
We formulate the Leray problem for inhomogeneous fluids in two dimensions and outline the proof of the existence of a solution. There are two kinds of results depending on whether the given value for the density is a continuous function or only an function. In the former case, the given densities are attained in the sense of uniform convergence and in the latter with respect to weak-* convergence.