Some remarks on a system of cross-diffusion equations with formal gradient flow structure

We study a system of cross-diffusion equations that results, as a formal limit, from an interacting particle system with multiple species. In the first part of the talk we exploit the (formal) gradient flow structure of the system to prove the existence of weak solutions. This is based on a priori bounds obtained from the dissipation of the corresponding entropy and the use of dual variables. In the second part, we discuss strong solutions and a weak-strong stability result under certain conditions on the diffusion constants.