In this talk, we look at a cross-diffusion system consisting of two Fokker-Planck equations where the gradient of the density for each species acts as a potential for the other one. The system is the gradient flow for the Wasserstein distance of a functional which is not lower semi-continuous, thus it is not well-posed. We then compute the convexification of the integral and provide an existence proof in a suitable sense for the gradient flow of the corresponding relaxed functional. The talk is based on a joint work with R. Ducasse and F. Santambrogio (Calc Var PDE, 2022).

https://arizona.zoom.us/j/82763762677