可压缩流体方程的熵谱与自组织动力学
Entropy Hierarchies for equations of compressible fluids and self-organized dynamics
摘要：
我们开发了一种方法，获得一个层次的新的高阶熵的上下文中的局部和非局部扩散和等熵压力的可压缩模型。当密度接近真空时，允许局部粘性退化。该方法提供了一个工具，传播初始正则性的经典解提供没有真空已经形成，并作为一种替代的经典能量方法。我们获得了一系列的全球适定性的结果，在以前发现的情况下，包括$p(ρ) = c_p ρ$的国家法律。作为应用，我们证明了基于主体的Cucker-Smale系统中带压力的集体行为模型的全局适定性。
英文摘要：
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 $p(ρ) = c_p ρ$. As an application we prove global well-posedness of collective behavior models with pressure arising from agent-based Cucker-Smale system.
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