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arXiv · 2510.07937

A cross-diffusion system with independent drifts and fast diffusion

Charles Elbar·Filippo Santambrogio
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Abstract

We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a fast-diffusion law with exponent $0< \alpha\le 1$ and different external potentials. For arbitrary non-negative $L^{1}$ initial data with bounded entropy and a mixing condition we prove the existence of global weak solutions. This extends the recent result of M\'esz\'aros, Parker from the linear diffusion ($\alpha=1$) to the fast-diffusion.

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Charles Elbar, Filippo Santambrogio. 2025-10-09. A cross-diffusion system with independent drifts and fast diffusion. https://arxiv.org/abs/2510.07937

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