Cross diffusion preventing blow up in the two-dimensional Keller-Segel model
Seminar Room 1, Newton Institute
We analyse the parabolic Keller-Segel system with an additional cross-diffusion term guaranteeing global-in-time existence of weak solutions for large data. This modification provides another helpful entropy dissipation term, which is used to show the global existence of solutions for any initial mass. For the proof we first analyse an approximate problem obtained from a semi-discretisation and a carefully chosen regularisation by adding higher order derivatives. Compactness arguments are used to carry out the limit to the original system. Our model also allows for further entropy estimates and may be helpful in numerical simulations to detect the occurence of blow-up.