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Publication 14-CNA-023
A Hybrid Variational Principle for the Keller-Segel System In $ \mathbb { R^2 }$ Adrien Blanchet Jose Antonio Carrillo David Kinderlehrer Michal Kowalczyk Philippe Laurencot Stefano Lisini Abstract: 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 |