logo_acta

Acta Mathematica Vietnamica

Gradient Flows of Modified Wasserstein Distances and Porous Medium Equations with Nonlocal Pressure

icon-email Nhan-Phu Chung , Quoc-Hung Nguyen

Abstract

We study families of porous medium equations 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.