Absence of gelation and regularity for coagulation-fragmentation-diffusion equations with critical coagulation rate in low dimension

Hector Bouton

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arXiv · 2609.22399

Absence of gelation and regularity for coagulation-fragmentation-diffusion equations with critical coagulation rate in low dimension

Hector Bouton

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Abstract

We consider a discrete coagulation-fragmentation-diffusion system on a bounded domain of $\mathbb{R}^d$. In dimension $d\leq 2$, we prove mass conservation (that is absence of gelation) when the coagulation coefficient satisfies the critical additive bound $a_{i, j} \leq C(i + j)$ for some constant $C > 0$. We thereby close the remaining gap between the spatially homogeneous setting and the spatially inhomogeneous diffusive setting. In dimension $d\leq 4$, we impose a higher decay rate on the coagulation and fragmentation coefficients, but we nonetheless prove regularity and absence of gelation under mild assumptions on the diffusion rates.

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Hector Bouton. 2026-09-18. Absence of gelation and regularity for coagulation-fragmentation-diffusion equations with critical coagulation rate in low dimension. https://arxiv.org/abs/2609.22399

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