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

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