Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts

Luca Alasio, Maria Bruna, Simone Fagioli +1

We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate-parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interac…