Work

On an inhomogeneous coagulation model with a differential sedimentation kernel

Year: 2025

Type: article

Abstract: We study an inhomogeneous coagulation equation that contains a transport term in the spatial variable modeling the sedimentation of clusters. We prove local existence of mass-conserving solutions for a class of coagulation kernels for which in the space homogeneous case instantaneous gelation (i.e., instantaneous loss of mass) occurs. Our result holds true in particular for sum-type kernels of homogeneity greater than one, for which solutions do not exist at all in the spatially homogeneous case. Moreover, our result covers kernels that in addition vanish on the diagonal, which have been used to model the onset of rain and the behavior of air bubbles in water.

Source: Annales de l Institut Henri Poincaré C Analyse Non Linéaire

DOI: 10.4171/aihpc/166

Authors: Iulia Cristian, Barbara Niethammer, Juan J. L. Velázquez

Institutions: Sorbonne Université, University of Bonn

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $700

Funders: Deutsche Forschungsgemeinschaft, Hausdorff Center for Mathematics