标题： 一维卡罗尔流体II: $C^1$ 爆破解准则 显示英文标题

标题： One-dimensional Carrollian fluids II: $C^1$ blow-up criteria

摘要： 卡罗来纳流体方程是在光速趋于零的极限下从相对论流体方程中得出的，在渐近对称性和平坦空间全息理论背景下，理论物理界最近对这些方程产生了浓厚的兴趣。 本文中，我们通过在一维空间中研究 $C^1$设置下的这些方程，开始了对这些方程的严格系统分析。 我们首先提出了一种等熵卡罗来纳方程的概念，并利用这一概念将卡罗来纳方程简化为一个 $2 \times 2$守恒律系统。 接着，我们采用拉克斯方案，然后分类了当等熵卡罗来纳方程的 $C^1$解在全球存在时，或在有限时间内爆破时的情况。 我们的分析假设了一个卡罗来纳能量密度的本构关系的卡罗来纳类比，指数范围在 $\gamma \in (1,3]$。 显示英文摘要

摘要： The Carrollian fluid equations arise from the equations for relativistic fluids in the limit as the speed of light vanishes, and have recently experienced a surge of interest in the theoretical physics community in the context of asymptotic symmetries and flat-space holography. In this paper we initiate the rigorous systematic analysis of these equations by studying them in one space dimension in the $C^1$ setting. We begin by proposing a notion of isentropic Carrollian equations, and use this to reduce the Carrollian equations to a $2 \times 2$ system of conservation laws. Using the scheme of Lax, we then classify when $C^1$ solutions to the isentropic Carrollian equations exist globally, or blow up in finite time. Our analysis assumes a Carrollian analogue of a constitutive relation for the Carrollian energy density, with exponent in the range $\gamma \in (1,3]$.