On the properties of weak solutions to elliptic equations with a drift term

We investigate weak solutions to the Dirichlet problem for an elliptic equation with a drift term having a sign-defined divergence. Under minimal assumptions on the smoothness of the drift, we present results on the existence, uniqueness and local properties of weak solutions, as well as the possible relation of these results with the Navier-Stokes theory. Based on a joint work with M. Chernobai.