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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 RN,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 RN. We also discuss steady-state smooth solutions of spherical symmetry to equation ().