In the two-dimensional Keller-Segel model for chemotaxis of biological cells,
blow-up of solutions in finite time occurs if the total mass is
above a critical value. Blow-up is a concentration event, where
point aggregates are created. In this work global existence of
generalized solutions is proven, allowing for measure valued
densities. This extends the solution concept after blow-up. The
existence result is an application of a theory developed by Poupaud,
where the cell distribution is characterized by an additional defect
measure, which vanishes for smooth cell densities. The global
solutions are constructed as limits of solutions of a regularized
A strong formulation is derived under the assumption that the generalized solution consists of a smooth part
and a number of smoothly varying point aggregates. Comparison with earlier formal asymptotic results shows
that the choice of a solution concept after blow-up is not unique and depends on the type of regularization.
This work is also concerned with local density profiles close to point aggregates. An equation for these
profiles is derived by passing to the limit in a rescaled version of the regularized model. Solvability
of the profile equation can also be obtained by minimizing a free energy functional.