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Symmetric Solutions to the Viscous Gas Equations

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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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Abstract

In the last decades, significant progress has been made on the existence and uniqueness of symmetric solutions to the compressible Navier-Stokes equations . In this chapter a brief review of some existence and large-time behavior results of symmetric (spherically symmetric, axisymmetric, etc) solutions with large data will be presented. The different cases: isentropic or nonisentropic flows, constant or the density-/temperature-dependent viscosity and heat conductivity, weak or strong (smooth) solutions, etc., will be discussed. The ideas and developed techniques used in analysis will be presented and analyzed, and some open questions will be addressed.

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Acknowledgements

Jiang is supported in part by the National Basic Research Program (Grant Nos. 2014CB745000, 2011CB309705), NSFC (Grant Nos. 11229101, 11371065), and Beijing Center for Mathematics and Information Interdisciplinary Sciences. Ju is supported by NSFC (Grant Nos. 11171035, 11571046, 11471028), the National Basic Research Program (Grant No. 2014CB745000) and BJNSF (Grant No. 1142001).

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  1. Institute of Applied Physics and Computational Mathematics, Beijing, China

    Song Jiang

  2. Institute of Applied Physics and Computational Mathematics, Beijing, China

    Qiangchang Ju

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  1. Tokyo, Tokyo, Japan

    Yoshikazu Giga

  2. Toulon, Var, France

    Antonin Novotny

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Jiang, S., Ju, Q. (2016). Symmetric Solutions to the Viscous Gas Equations. 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_35-1

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