One-dimensional Carrollian fluids III: Global existence and weak continuity in L∞$L^\infty$

The Carrollian fluid equations arise as the (Formula presented.) 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 ((Formula presented.)). 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 (Formula presented.), and establish a kinetic formulation of the problem. This global existence result in (Formula presented.) extends the (Formula presented.) theory presented in [2].