Symmetric Solutions to the Viscous Gas Equations

Song Jiang () and Qiangchang Ju ()
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Song Jiang: Institute of Applied Physics and Computational Mathematics
Qiangchang Ju: Institute of Applied Physics and Computational Mathematics

Chapter 33 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 1711-1749 from Springer

Abstract: Abstract In the last decades, significant progress has been made on the existence and uniqueness of symmetric solutions to the compressible Navier-Stokes equations 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.

Date: 2018
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DOI: 10.1007/978-3-319-13344-7_35

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