One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in L^∞

The Carrollian fluid equations arise as the c → 0 limit of the relativistic fluid equations and have recently experienced a surge of activity in the flat-space holography community. However, the rigorous mathematical well-posedness theory for these equations does not appear to have been previously studied. This paper is the third in a series in which we initiate the systematic analysis of the Carrollian fluid equations. In the present work we prove the global-in-time existence of bounded entropy solutions to the isentropic Carrollian fluid equations in one spatial dimension for a particular constitutive law (γ = 3). Our method is to use a vanishing viscosity approximation for which we establish a compensated compactness framework. Using this framework we also prove the compactness of entropy solutions in L^∞, and establish a kinetic formulation of the problem. This global existence result in L^∞ extends the C¹ theory presented in our companion paper ``One-Dimensional Carrollian Fluids II: C¹ Blow-up Criteria''.