TY - JOUR
T1 - Thermodynamically consistent modeling for complex fluids and mathematical analysis
AU - Suzuki, Yukihito
AU - Ohnawa, Masashi
AU - Mori, Naofumi
AU - Kawashima, Shuichi
N1 - Funding Information:
Financial supports from the Grants-in-Aid for Scientific Research (KAKENHI, Grant Number 19H05597, 18H01131, 17K05376, 17K05313, 15KT0014) of the Japan Society for the Promotion of Science (JSPS), Interdisciplinary Institute for Thermal Energy Conversion Engineering and Mathematics, Organization for University Research Initiatives at Waseda University, and Railway Technical Research Institute are gratefully acknowledged.
Publisher Copyright:
© 2021 World Scientific Publishing Company.
PY - 2021/9/1
Y1 - 2021/9/1
N2 - The goal of this paper is to derive governing equations for complex fluids in a thermodynamically consistent way so that the conservation of energy and the increase of entropy is guaranteed. The model is a system of first-order partial differential equations on density, velocity, energy (or equivalently temperature), and conformation tensor. A barotropic model is also derived. In the one-dimensional case, we express the barotropic model in the form of hyperbolic balance laws, and show that it satisfies the stability condition. Consequently, the global existence of solutions around equilibrium states is proved and the convergence rates is obtained.
AB - The goal of this paper is to derive governing equations for complex fluids in a thermodynamically consistent way so that the conservation of energy and the increase of entropy is guaranteed. The model is a system of first-order partial differential equations on density, velocity, energy (or equivalently temperature), and conformation tensor. A barotropic model is also derived. In the one-dimensional case, we express the barotropic model in the form of hyperbolic balance laws, and show that it satisfies the stability condition. Consequently, the global existence of solutions around equilibrium states is proved and the convergence rates is obtained.
KW - Complex fluids
KW - Stability
KW - Thermodynamic consistency
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U2 - 10.1142/S0218202521500421
DO - 10.1142/S0218202521500421
M3 - Article
AN - SCOPUS:85118511171
VL - 31
SP - 1919
EP - 1949
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 10
ER -