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arXiv · 2409.08441

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

Nhan-Phu Chung·Thanh-Son Trinh
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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.

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Nhan-Phu Chung, Thanh-Son Trinh. 2024-09-13. Modified Wasserstein gradient flow formulation of time-fractional porous medium equations with nonlocal pressure. https://arxiv.org/abs/2409.08441

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