On the blow-up phenomena of solutions for the full compressible Euler equations in RN

In fluid dynamics, blow-up phenomena of solutions is interesting and challenging to physicists and mathematicians. The present paper is devoted to studying blow-up phenomena of the spherically symmetric solutions for the full compressible Euler equations in R-N, N >= 1. The approach is to a construct special explicit solution with spherical symmetry to study certain blow-up phenomena of solutions to the full compressible Euler equation in R-N. We also discuss steady-state smooth solutions of spherical symmetry to equation (1.1).