Symmetric solutions to the viscous gas equations

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.