一维卡罗尔流体 III：L^∞ 中的全局存在性与弱连续性
One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^\infty$
AI总结：
本文针对一维等熵卡罗尔流体方程（γ=3），利用消失粘性近似和补偿紧性框架，证明了有界熵解在 L^∞ 中的全局时间存在性与紧性，并建立了动力学表述，扩展了此前 C^1 爆破判据理论。
摘要：
卡罗尔流体方程作为相对论流体方程在 c → 0 极限下的结果而出现，近年来在平坦空间全息对偶领域引起了大量关注。然而，这些方程的严格数学适定性理论此前似乎尚未被研究过。本文是我们系统分析卡罗尔流体方程系列中的第三篇。在本文中，我们针对一种特定的本构关系（γ = 3），证明了一维空间等熵卡罗尔流体方程的有界熵解在时间上全局存在。我们的方法是使用消失粘性近似，并为其建立补偿紧性框架。利用该框架，我们还证明了熵解在 L^∞ 中的紧性，并建立了该问题的动力学表述。这一 L^∞ 中的全局存在性结果扩展了我们在姊妹篇论文《一维卡罗尔流体 II：C^1 爆破判据》中提出的 C^1 理论。
英文摘要：
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 ($γ= 3$). 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 $L^\infty$, 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''.
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