A hybrid variational principle for the Keller-Segel system in $\mathbb   R^2$
  We construct weak global in time solutions to the classical Keller-Segel system cell movement by chemotaxis in two dimensions when the total mass is below the well-known critical value. Our construction takes advantage of the fact that the Keller-Segel system can be realized as a gradient flow in a suitable functional product space. This allows us to employ a hybrid variational principle which is a generalisation of the minimising implicit scheme for Wasserstein distances introduced by Jordan, Kinderlehrer and Otto (1998). 
Adrien Blanchet (GREMAQ), Jos\'e A. Carrillo, David Kinderlehrer,   Michal Kowalczyk (DIM), Philippe Lauren\c{c}ot (IMT), St...
math.AP