Thermodynamically consistent modeling for complex fluids and mathematical analysis

Yukihito Suzuki, Masashi Ohnawa*, Naofumi Mori, Shuichi Kawashima

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1919-1949
Number of pages31
JournalMathematical Models and Methods in Applied Sciences
Issue number10
Publication statusPublished - 2021 Sep 1


  • Complex fluids
  • Stability
  • Thermodynamic consistency

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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