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arXiv · 1908.01784

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

Peter Constantin·Theodore D. Drivas·Roman Shvydkoy
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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.

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Peter Constantin, Theodore D. Drivas, Roman Shvydkoy. 2019-08-05. Entropy Hierarchies for equations of compressible fluids and self-organized dynamics. https://arxiv.org/abs/1908.01784

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