标题： 一维卡罗尔流体 III：$L^\infty$中的整体存在性和弱连续性 显示英文标题

标题： One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^\infty$

摘要： 卡罗尔流体方程作为相对论流体方程的$c \to 0$极限出现，并且最近在平空间全息理论领域引起了广泛关注。 然而，这些方程的严格数学适定性理论似乎此前尚未被研究。 本文是系列论文的第三篇，在其中我们开始对卡罗尔流体方程进行系统分析。 在本工作中，我们证明了在一维空间中，对于特定的本构定律（$\gamma = 3$），等熵卡罗尔流体方程有界熵解的全局时间存在性。 我们的方法是使用一个消失粘性近似，并为此建立了一个补偿紧性框架。 利用这个框架，我们也证明了熵解在$L^\infty$中的紧性，并建立了该问题的粒子动力学表述。 这一在$L^\infty$中的全局存在结果扩展了我们在配套论文《一维卡罗尔流体 II：$C^1$爆炸条件》中提出的$C^1$理论。 显示英文摘要

摘要： The Carrollian fluid equations arise as the $c \to 0$ 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 ($\gamma = 3$). 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 $L^\infty$, and establish a kinetic formulation of the problem. This global existence result in $L^\infty$ extends the $C^1$ theory presented in our companion paper ``One-Dimensional Carrollian Fluids II: $C^1$ Blow-up Criteria''.