We consider porous medium equations with a drift term of divergence type, and establish existence of non-negative L^q weak solutions, provided that the drift belongs to a scaling invariant class.
The main result is to construct weak solutions satisfying not only an energy inequality but also moment and speed estimates. One of the main tools is the splitting method in order to allow a sequence of approximated solutions, which implies, by passing to the limit, the existence of weak solutions. As an application, we present some examples of Keller-Segel equations of porous medium type whose known existence and regularity results are consequently improved.