A cross-diffusion system with independent drifts and fast diffusion

Abstract

We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a fast-diffusion law with exponent $0< α\le 1$ and different external potentials. For arbitrary non-negative $L^{1}$ initial data with bounded entropy and a mixing condition we prove the existence of global weak solutions. This extends the recent result of Mészáros, Parker from the linear diffusion ($α=1$) to the fast-diffusion.