Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow

TL;DR

This paper establishes the existence and uniqueness of measure solutions for a system of continuity equations with non-local flow, providing a foundational mathematical result for such systems.

Contribution

It proves existence and uniqueness of measure solutions for the continuity system with non-local flow and offers stability results under parameter variations.

Findings

Existence of measure solutions confirmed.

Uniqueness of solutions established.

Stability with respect to parameters demonstrated.

Abstract

In this paper, we prove existence and uniqueness of measure solutions for the Cauchy problem associated to the (vectorial) continuity equation with a non-local flow. We also give a stability result with respect to various parameters.