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Publication 87

A Hybrid Variational Principle for the Keller-Segel System in R2


Adrien Blanchet
TSE (GREMAQ, Universite Toulouse 1 Capitole)
Toulouse, France

Jose Antonio Carrillo
Department of Mathematics
Imperial College London

CMUDavid Kinderlehrer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Michal Kowalczyk
Departamento de Ingeniera Matematica and Centro de Modelamiento Matematico (UMI 2807 CNRS)
Universidad de Chile, Casilla Santiago, Chile

Philippe Laurencot
Institut de Mathematiques de Toulouse
Toulouse, France

Stefano Lisini
Dipartimento di Matematica "F. Casorati"
Universita degli Studi di Pavia
Pavia, Italy

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).
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