One-dimensional Carrollian fluids II: $C^1$ blow-up criteria
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914258932989952 |
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| author | Athanasiou, Nikolaos Petropoulos, P. Marios Schulz, Simon Taujanskas, Grigalius |
| author_facet | Athanasiou, Nikolaos Petropoulos, P. Marios Schulz, Simon Taujanskas, Grigalius |
| contents | 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 $γ\in (1,3]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-dimensional Carrollian fluids II: $C^1$ blow-up criteria Athanasiou, Nikolaos Petropoulos, P. Marios Schulz, Simon Taujanskas, Grigalius Analysis of PDEs General Relativity and Quantum Cosmology High Energy Physics - Theory 35B44, 35L40, 35Q35, 35Q75, 85A30 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 $γ\in (1,3]$. |
| title | One-dimensional Carrollian fluids II: $C^1$ blow-up criteria |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology High Energy Physics - Theory 35B44, 35L40, 35Q35, 35Q75, 85A30 |
| url | https://arxiv.org/abs/2407.05971 |