Almost everywhere well-posedness of continuity equations with measure initial data

TL;DR

This paper presents new results on the well-posedness and stability of continuity equations with measure initial data, emphasizing 'almost everywhere' conditions, with proofs and applications to quantum mechanics.

Contribution

It introduces novel results on the well-posedness and stability of continuity equations with measure initial data, extending previous work.

Findings

Established 'almost everywhere' well-posedness results

Proved stability of solutions under measure initial data

Applied results to semiclassical limit of Schrödinger equation

Abstract

The aim of this note is to present some new results concerning "almost everywhere" well-posedness and stability of continuity equations with measure initial data. The proofs of all such results can be found in \cite{amfifrgi}, together with some application to the semiclassical limit of the Schr\"odinger equation.