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

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).

References in corpus (2)

• Stable blow-up dynamic for the parabolic-parabolic Patlak-Keller-Segel model
• Trudinger-Moser inequality on the whole plane with the exact growth condition

Cited by in corpus (4)

• A note on the variational analysis of the parabolic-parabolic Keller-Segel system in one spatial dimension
• A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations
• Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations
• Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure