Year: 2025
Type: preprint
Abstract: Motivated by the recent results of Andreis-Iyer-Magnanini (2023), we provide a short proof, revisiting the one of Escobedo-Mischler-Perthame (2002), that for a large class of coagulation kernels, any weak solution to the Smoluchowski equation looses mass in finite time. The class of kernels we consider is essentially the same as the one of Andreis-Iyer-Magnanini (2023): homogeneous kernels of degree $γ>1$ not vanishing on the diagonal, or homogeneous kernels of degree $γ=1$ not vanishing on the diagonal with some additional logarithmic factor. We also show that when $γ=1$, the power of the logarithmic factor ensuring gelation may depend on the shape of the kernel.
Source: arXiv (Cornell University)
Author: Fournier, Nicolas
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406192587