  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).
