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

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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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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.

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, Japan

    Akitaka Matsumura

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  1. Akitaka Matsumura
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Correspondence to Akitaka Matsumura .

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Editors and Affiliations

  1. Tokyo, Tokyo, Japan

    Yoshikazu Giga

  2. Toulon, Var, France

    Antonin Novotny

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Matsumura, A. (2016). Waves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact Waves. In: Giga, Y., Novotny, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-10151-4_60-1

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  • DOI: https://doi.org/10.1007/978-3-319-10151-4_60-1

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  • Online ISBN: 978-3-319-10151-4

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