The global existence and blowup of the classical solution to the relativistic dust in a FLRW geometry

This paper is concerned with the global existence and blowup of the classical solution to the Cauchy problem of the relativistic Euler equation with $p=0$ in a fixed Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. The aim of this work is to study clearly the effect of the expansion rate of the spacetime on the life span of the classical solution to the pressureless fluid. Since the density and the velocity of the relativistic dust admits the same principal part, we can obtain much more accurate results by the characteristic method rather than energy estimates.