Local well posedness for a linear coagulation equation

TL;DR

This paper establishes local well-posedness for a class of linear coagulation equations with fluxes, providing a priori estimates and discussing regularizing effects in large particle sizes.

Contribution

It introduces new a priori estimates that enable proving local well-posedness for linear coagulation equations with particle fluxes.

Findings

Proved local well-posedness of the equations.

Identified regularizing effects for large particle sizes.

Derived key a priori estimates for the equations.

Abstract

In this paper we derive some a priori estimates for a class of linear coagulation equations with particle fluxes towards large size particles. The derived estimates allow us to prove local well posedness for the considered equations. Some regularizing effects exhibited by the equations in the particle distributions for large particle sizes are discussed in detail.