Singularities in finite time of the full compressible Euler equations in [formula omitted

Abstract

The present article is concerned with the study of blow-up phenomena of the smoooth solutions for the full compressible Euler equations in Rd,d≥1, which have always been a great concern to physicists and mathematicians throughout history. The approach is to construct exact explicit function to study singularities in finite time of the spherically symmetric solutions, provided the initial data satisfy some conditions. Compared with the results obtained by Sideris in 1984 (CMP), in this article, the initial velocity field is not required to have a compact support and the initial density and entropy is not equal to a constant outside the support of the initial velocity field.