Finite upper bounds of existence time of classical solutions to relativistic Euler equations with finite energy

Abstract In this paper, we consider the relativistic Euler equations with vacuum state and finite energy such that the existence of local classical solutions is guaranteed by smooth enough initial data. We first show that the propagation speed of support of classical solutions is at most by considering the non‐vacuum case with a perturbation, where represents the derivative of the pressure function with respect to the density. It follows that the support does not expand in most cases where one has . Subsequently, by introducing a weighted second moment of inertia and a weighted radial component of momentum, we prove that the classical solutions of the relativistic Euler equations with vacuum state and finite energy can only exist up to a finite time. Moreover, a class of concrete finite upper bounds of existence time that depends only on initial data and given parameters is established. Last, we provide specific examples of our test functions.