A kinetic model for coagulation-fragmentation

TL;DR

This paper proves an existence theorem for a kinetic coagulation-fragmentation model using renormalized solutions and weak-compactness methods, addressing initial data constraints and finite particle assumptions.

Contribution

It introduces an existence proof for the coagulation-fragmentation kinetic model under realistic physical bounds and finite norms, employing renormalized solutions and advanced compactness techniques.

Findings

Existence of solutions under physical bounds

Use of renormalized solutions for non-smooth data

Propagation of finite $L^p$-norms

Abstract

The aim of this paper is to show an existence theorem for a kinetic model of coagulation-fragmentation with initial data satisfying the natural physical bounds, and assumptions of finite number of particles and finite $L^p$-norm. We use the notion of renormalized solutions introduced dy DiPerna and Lions, because of the lack of \textit{a priori} estimates. The proof is based on weak-compactness methods in $L^1$, allowed by $L^p$-norms propagation.