# Entropy Hierarchies for equations of compressible fluids and self-organized dynamics

## TL;DR

This paper introduces a hierarchy of higher-order entropies for compressible fluid models with diffusion and pressure, enabling new global well-posedness results and applications to collective behavior models.

## Contribution

It develops a novel method to generate entropy hierarchies, providing an alternative to energy methods and extending well-posedness results to new cases.

## Key findings

- Established global well-posedness for models with $p(\rho) = c_p \rho$
- Proved well-posedness for collective behavior models with pressure
- Provided a new tool for propagating initial regularity in compressible fluids

## Abstract

We develop a method of obtaining a hierarchy of new higher-order entropies in the context of compressible models with local and non-local diffusion and isentropic pressure. The local viscosity is allowed to degenerate as the density approaches vacuum. The method provides a tool to propagate initial regularity of classical solutions provided no vacuum has formed and serves as an alternative to the classical energy method. We obtain a series of global well-posedness results for state laws in previously uncovered cases including $p(\rho) = c_p \rho$. As an application we prove global well-posedness of collective behavior models with pressure arising from agent-based Cucker-Smale system.