SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 3073-3092, January 2020.
We develop a method of obtaining a hierarchy of new higher-order entropies in the context of compressible models with local and nonlocal 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 an agent-based Cucker--Smale system.

中文翻译：

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可压缩流体方程的熵层次和自组织动力学

SIAM数学分析杂志，第52卷，第3期，第3073-3092页，2020年1月。
我们开发了一种在具有局部和非局部扩散以及等熵压力的可压缩模型的背景下，获取新的高阶熵的层次结构的方法。当密度接近真空时，允许局部粘度退化。该方法提供了传播经典解的初始规则性的工具，前提是尚未形成真空，并且可以用作经典能量方法的替代方法。在以前未发现的情况下，我们获得了一系列针对州法律的全局适定性结果，包括$ p（\ rho）= c_p \ rho $。作为应用程序，我们证明了集体行为模型的全局适定性，其基于基于代理的Cucker-Smale系统所产生的压力。