Generalized hydrodynamics and the classical hydrodynamic limit

Zaibao Yang Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, China, 100084 Wen-An Yong Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China Yi Zhu Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, China, 100084

Analysis of PDEs mathscidoc:2204.03004

2018.2
This work is concerned with our recently developed formalism of non-equilibrium thermodynamics. This formalism extends the classical irreversible thermodynamics which leads to classical thermodynamics and can not describe physical phenomena with long relaxations. With the extended theory, we obtain a generalized hydrodynamic system which can be used to describe the non-Newtonian fluids, heat transfer beyond Fourier's law and fluid flow in very short temporal and spatial scales. We study the mathematical structure of the generalized hydrodynamic system and show that it possesses a nice conservation-dissipation structure and therefore is symmetrizable hyperbolic. Moreover, we rigorously justify that this generalized hydrodynamic system tends to the classical hydrodynamics when the relaxation times approach to zero. This shows that the classical hydrodynamics can be derived as an approximation of our generalized one.
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@inproceedings{zaibao2018generalized,
  title={Generalized hydrodynamics and the classical hydrodynamic limit},
  author={Zaibao Yang, Wen-An Yong, and Yi Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220422142434417375101},
  year={2018},
}
Zaibao Yang, Wen-An Yong, and Yi Zhu. Generalized hydrodynamics and the classical hydrodynamic limit. 2018. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220422142434417375101.
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