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arXiv · 2610.25818

Global weak solutions for a two-species Riesz cross-attraction system with quadratic diffusion

Zhenxing Liu·Shen Bian
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Abstract

We establish global existence for a two-species cross-attraction system on $\mathbb R^3$, with quadratic diffusion and the common interaction operator $(-Δ)^{-s}$, where $1/2<s<1$. Nonnegative initial data in $L^1\cap L^\infty$ with finite second moments require no smallness condition on the masses. A joint energy and second-moment estimate and a coupled $L^p$ iteration give uniform a priori estimates for the regularized solutions. Compactness then yields mass-conserving global weak solutions, bounded on every finite time interval and strongly continuous in $L^1\cap L^2$. The energy inequality holds at every pair of time endpoints. Uniqueness and bounds uniform for all positive times are not asserted.

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Zhenxing Liu, Shen Bian. 2026-10-19. Global weak solutions for a two-species Riesz cross-attraction system with quadratic diffusion. https://arxiv.org/abs/2610.25818

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