Modified Wasserstein gradient flow formulation of time-fractional porous medium equations with nonlocal pressure

TL;DR

This paper introduces a novel approach to solving time-fractional porous medium equations with nonlocal pressure using a modified Wasserstein gradient flow scheme, demonstrating existence, regularization, and norm estimates.

Contribution

It develops a new JKO scheme based on a modified Wasserstein distance and fractional Sobolev norm for these equations, establishing existence and regularization results.

Findings

Existence of weak solutions via the proposed scheme

Regularization effects demonstrated

L^p norm estimates established

Abstract

We consider a class of time-fractional porous medium equations with nonlocal pressure. We show the existence of their weak solutions by proposing a JKO scheme for modified Wasserstein distance and a square fractional Sobolev norm. Moreover, the regularization effect and the Lp norm estimate are established in this paper.