One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^\infty$ - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

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

Simon Schulz
  • Fonction : Auteur
Grigalius Taujanskas
  • Fonction : Auteur

Résumé

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''.

Dates et versions

hal-04659642 , version 1 (23-07-2024)

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Citer

P. Marios Petropoulos, Simon Schulz, Grigalius Taujanskas. One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^\infty$. 2024. ⟨hal-04659642⟩
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