Gradient flows of modified Wasserstein distances and porous medium equations with nonlocal pressure

Abstract

We study families of porous medium equation with nonlocal pressure. We construct their weak solutions via JKO schemes for modified Wasserstein distances. We also establish the regularization effect and decay estimates for the $L^p$ norms.

24 pages. Dedicated to Professor Duong Minh Duc on the occasion of his 70th birthday. Comments welcome