One-dimensional Carrollian fluids II: C1 blow-up criteria

The Carrollian fluid equations arise from the equations for relativistic fluids in the limit as the speed of light vanishes, and have recently experienced a surge of interest in the theoretical physics community in the context of asymptotic symmetries and flat-space holography. In this paper, we initiate the rigorous systematic analysis of these equations by studying them in one space dimension in the (Formula presented.) setting. We begin by proposing a notion of isentropic Carrollian equations, and use this to reduce the Carrollian equations to a (Formula presented.) system of conservation laws. Using the scheme of Lax, we then classify when (Formula presented.) solutions to the isentropic Carrollian equations exist globally, or blow up in finite time. Our analysis assumes a Carrollian analogue of a constitutive relation for the Carrollian energy density, with exponent in the range (Formula presented.).