On the parabolic-elliptic limit of the doubly parabolic Keller--Segel   system modelling chemotaxis
  We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller--Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption. 
Piotr Biler, Lorenzo Brandolese (ICJ)