Acta Mathematica Vietnamica
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Gradient Flows of Modified Wasserstein Distances and Porous Medium Equations with Nonlocal Pressure
Nhan-Phu Chung , Quoc-Hung Nguyenpp. 209-235
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.