Thermodynamically consistent modeling for complex fluids and mathematical analysis

被引：2

作者：

Suzuki, Yukihito ^{[1
]}

Ohnawa, Masashi ^{[2
]}

Mori, Naofumi ^{[2
]}

Kawashima, Shuichi ^{[3
]}

机构：

[1] Aomori Univ, Fac Software & Informat Technol, Aomori 0300943, Japan

[2] Tokyo Univ Marine Sci & Technol, Dept Ocean Sci, Tokyo 1088477, Japan

[3] Waseda Univ, Fac Sci & Engn, Tokyo 1698555, Japan

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2021年 / 31卷 / 10期

基金：

日本学术振兴会;

关键词：

Complex fluids; thermodynamic consistency; stability; DISSIPATIVE HYPERBOLIC SYSTEMS; GLOBAL EXISTENCE; VISCOELASTIC FLUIDS; CONSTITUTIVE EQUATION; CONSERVATION-LAWS; PARABOLIC-SYSTEMS; SMOOTH SOLUTIONS; ENTROPY; DERIVATION; DYNAMICS;

D O I：

10.1142/S0218202521500421

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1919 / 1949

页数：31

共 48 条

[1]

[Anonymous], 2005, EQUILIBRIUM THERMODY

[2]

[Anonymous], 1987, Dynamics of Polymeric Liquids, Vol

[3] Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers [J].