Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 14-CNA-023 A Hybrid Variational Principle for the Keller-Segel System In $\mathbb { R^2 }$ Adrien BlanchetTSE (GREMAQ, Universite Toulouse 1 Capitole) Toulouse, FranceAdrien.Blanchet@ut-capitole.fr José Antonio CarrilloDepartment of Mathematics Imperial College London Londoncarrillo@imperial.ac.uk David KinderlehrerDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213davidk@andrew.cmu.edu Michal KowalczykDepartamento de Ingeniera Matematica and Centro de Modelamiento Matematico (UMI 2807 CNRS) Universidad de Chile, Casilla Santiago, Chilekowalczy@dim.uchile.cl Philippe LaurençotInstitut de Mathematiques de Toulouse Toulouse, FrancePhilippe.Laurencot@math.univ-toulouse.fr Stefano LisiniDipartimento di Matematica "F. Casorati" Universita degli Studi di Pavia Pavia, Italystefano.lisini@unipv.itAbstract: 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).Get the paper in its entirety as  14-CNA-023.pdf