@article{223f3976721948cc8e3a6ff8acf884d2,
title = "The brinkman-fourier system with ideal gas equilibrium",
abstract = "In this work, we will introduce a general framework to derive the thermodynamics of a fluid mechanical system, which guarantees the consistence between the energetic variational approaches with the laws of thermodynamics. In particular, we will focus on the coupling between the thermal and mechanical forces. We follow the framework for a classical gas with ideal gas equilibrium and present the existences of weak solutions to this thermodynamic system coupled with the Brinkman-type equation to govern the velocity field.",
author = "Chun Liu and Sulzbach, {Jan Eric}",
note = "Funding Information: Acknowledgments. The authors would like to thank Prof. Anja Schl{\"o}merkemper for constructive suggestions and discussions. This research was supported in part by the National Science Foundation Grant NSF DMS–1714401 and the United States–Israel Binational Science Foundation Grant BSF 2024246. Funding Information: 2020 Mathematics Subject Classification. Primary: 35D30, 35Q79; Secondary: 76N10. Key words and phrases. Brinkman-Fourier system, temperature effects, ideal gas equilibrium, free energy, existence of weak solutions. The authors are supported by NSF grant DMS-1714401 and by United States-Israel Binational Science Foundation grant BSF 2024246. ∗ Corresponding author: Jan-Eric Sulzbach. Publisher Copyright: {\textcopyright} 2022 American Institute of Mathematical Sciences. All rights reserved.",
year = "2022",
month = jan,
doi = "10.3934/dcds.2021123",
language = "English (US)",
volume = "42",
pages = "425--462",
journal = "Discrete and Continuous Dynamical Systems",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "1",
}