Waves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact Waves

Akitaka Matsumura ()
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Akitaka Matsumura: Osaka University, Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology

Chapter 44 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 2495-2548 from Springer

Abstract: Abstract This short article focuses on several one-dimensional model systems which often appear in the field of compressible viscous fluids, and discusses their Cauchy problems with prescribed far-field states. In particular, it describes the asymptotic behavior of the solutions in relation to the Riemann problems for the hyperbolic parts with the same far-field states. It has been expected that the solutions tend toward various asymptotic wave patterns as time goes to infinity, that is, various combinations of viscous shock, rarefaction, and contact waves. Many cases have been mathematically justified, but many others still remain open. The intent of this article is to give the reader introductory insights into how various primitive energy methods have contributed to the mathematical justifications, through some specific topics.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-13344-7_60

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DOI: 10.1007/978-3-319-13344-7_60

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