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Symmetric Solutions to the Viscous Gas Equations

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Author

Listed:
  • Song Jiang

    (Institute of Applied Physics and Computational Mathematics)

  • Qiangchang Ju

    (Institute of Applied Physics and Computational Mathematics)

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.

Suggested Citation

  • Song Jiang & Qiangchang Ju, 2018. "Symmetric Solutions to the Viscous Gas Equations," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 33, pages 1711-1749, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_35
    DOI: 10.1007/978-3-319-13344-7_35
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