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arXiv · 1407.5562

A hybrid variational principle for the Keller-Segel system in $\mathbb R^2$

Adrien Blanchet·José A. Carrillo·David Kinderlehrer·Michal Kowalczyk·Philippe Laurençot·Stefano Lisini
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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).

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Adrien Blanchet, José A. Carrillo, David Kinderlehrer, Michal Kowalczyk, Philippe Laurençot, Stefano Lisini. 2014-07-21. A hybrid variational principle for the Keller-Segel system in $\mathbb R^2$. https://arxiv.org/abs/1407.5562

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