Flow Solutions of Transport Equations

TL;DR

This paper discusses the construction of forward untangled flows under broad conditions, ensuring the well-posedness of associated transport equations, which is fundamental for understanding fluid dynamics and related transport phenomena.

Contribution

It introduces a method to construct forward untangled flows under general assumptions, establishing well-posedness of the transport problem in this context.

Findings

Existence of forward untangled flows under broad conditions

Well-posedness of transport equations associated with these flows

Framework applicable to various fluid dynamics scenarios

Abstract

Under general assumptions on the velocity field, it is possible to construct a flow that is forward untangled. Once such a flow has been selected, the associated transport problem is well-posed.