# An Overview on Some Results Concerning the Transport Equation and its Applications to Conservation Laws

## TL;DR

This paper provides an informal overview of the theory of transport equations with non-smooth velocity fields and explores their applications to the well-posedness of hyperbolic conservation laws.

## Contribution

It offers a comprehensive summary of recent results on transport equations with irregular velocities and their implications for conservation law problems.

## Key findings

- Insights into the well-posedness of hyperbolic systems
- Connections between transport equations and conservation laws
- Summary of recent theoretical developments

## Abstract

We provide an informal overview on the theory of transport equations with non smooth velocity fields, and on some applications of this theory to the well-posedness of hyperbolic systems of conservation laws.