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Initial–boundary-value problems for one-dimensional compressible Navier–Stokes equations with degenerate transport coefficients

Part of: Compressible fluids and gas dynamics, general Equations of mathematical physics and other areas of application Representations of solutions

Published online by Cambridge University Press:  16 March 2017

Qing Chen ,
Huijiang Zhao  and
Qingyang Zou
Qing Chen
Affiliation:
School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, People's Republic of China (chenqing@xmut.edu.cn)
Huijiang Zhao
Affiliation:
School of Mathematics and Statistics, and Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, People's Republic of China (hhjjzhao@hotmail.com)
Qingyang Zou
Affiliation:
College of Science, Wuhan University of Science and Technology, Wuhan 430081, People's Republic of China (qyzou@whu.edu.cn)
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Extract

This paper is concerned with the construction of global, non-vacuum, strong, large amplitude solutions to initial–boundary-value problems for the one-dimensional compressible Navier–Stokes equations with degenerate transport coefficients. Our analysis derives the positive lower and upper bounds on the specific volume and the absolute temperature.

Keywords

one-dimensional compressible Navier–Stokes equationsinitial–boundary-value problemsglobal solutions with large datadegenerate transport coefficients

MSC classification

Secondary: 35D35: Strong solutions 35Q35: PDEs in connection with fluid mechanics 76N10: Existence, uniqueness, and regularity theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 5 , October 2017 , pp. 935 - 969
Copyright
Copyright © Royal Society of Edinburgh 2017 

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