@article{d4a4d087113d4e6cb22ab48ec6a365d9,
title = "Entropy hierarchies for equations of compressible fluids and self-organized dynamics",
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. ",
keywords = "Alignment, Compressible Navier-Stokes, Cucker-Smale, Flocking, Fractional diffusion",
author = "Peter Constantin and Drivas, {Theodore D.} and Roman Shvydkoy",
note = "Funding Information: \ast Received by the editors August 5, 2019; accepted for publication (in revised form) April 15, 2020; published electronically June 30, 2020. https://doi.org/10.1137/19M1278983 Funding: The research of the first author was partially supported by NSF grant DMS-1713985. The research of the second author was partially supported by NSF grant DMS-1703997. The research of the third author was supported in part by NSF grants DMS 1515705 and DMS-1813351 and the Simons Foundation. \dagger Department of Mathematics, Princeton University, Princeton, NJ 08544 (const@math.princeton. edu, tdrivas@math.princeton.edu). \ddagger Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607 (shvydkoy@uic.edu). Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics.",
year = "2020",
doi = "10.1137/19M1278983",
language = "English (US)",
volume = "52",
pages = "3073--3092",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}