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

Peter Constantin, Theodore Dimitrios Drivas, Roman Shvydkoy

Research output: Contribution to journalArticlepeer-review

Abstract

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(ρ) = cpρ. As an application we prove global well-posedness of collective behavior models with pressure arising from an agent-based Cucker-Smale system.

Original languageEnglish (US)
Pages (from-to)3073-3092
Number of pages20
JournalSIAM Journal on Mathematical Analysis
Volume52
Issue number3
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Alignment
  • Compressible Navier-Stokes
  • Cucker-Smale
  • Flocking
  • Fractional diffusion

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