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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2511.09800 |
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| _version_ | 1866908716818759680 |
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| author | Liu, Jian-Guo Pego, Robert L. |
| author_facet | Liu, Jian-Guo Pego, Robert L. |
| contents | In cosmology, a basic explanation of the observed concentration of mass in singular structures is provided by the Zeldovich approximation, which takes the form of free-streaming flow for perturbations of a uniform Einstein-de Sitter universe in co-moving coordinates. The adhesion model suppresses multi-streaming by introducing viscosity. We study mass flow in this model by analysis of Lagrangian advection in the zero-viscosity limit. Under mild conditions, we show that a unique limiting Lagrangian semi-flow exists. Limiting particle paths stick together after collision and are characterized uniquely by a differential inclusion. The absolutely continuous part of the mass measure agrees with that of a Monge-Ampère measure arising by convexification of the free-streaming velocity potential. But the singular parts of these measures can differ when flows along singular structures merge, as shown by analysis of a 2D Riemann problem. The use of Monge-Ampère measures and optimal transport theory for the reconstruction of inverse Lagrangian maps in cosmology was introduced in work of Brenier & Frisch et al. (Month. Not. Roy. Ast. Soc. 346, 2003). In a neighborhood of merging singular structures in our examples, however, we show that reconstruction yielding a monotone Lagrangian map cannot be exact a.e., even off of the singularities themselves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of the adhesion model and the reconstruction problem in cosmology Liu, Jian-Guo Pego, Robert L. Analysis of PDEs Mathematical Physics 35Q85, 85A40, 39A60, 49Q22, 34A60 In cosmology, a basic explanation of the observed concentration of mass in singular structures is provided by the Zeldovich approximation, which takes the form of free-streaming flow for perturbations of a uniform Einstein-de Sitter universe in co-moving coordinates. The adhesion model suppresses multi-streaming by introducing viscosity. We study mass flow in this model by analysis of Lagrangian advection in the zero-viscosity limit. Under mild conditions, we show that a unique limiting Lagrangian semi-flow exists. Limiting particle paths stick together after collision and are characterized uniquely by a differential inclusion. The absolutely continuous part of the mass measure agrees with that of a Monge-Ampère measure arising by convexification of the free-streaming velocity potential. But the singular parts of these measures can differ when flows along singular structures merge, as shown by analysis of a 2D Riemann problem. The use of Monge-Ampère measures and optimal transport theory for the reconstruction of inverse Lagrangian maps in cosmology was introduced in work of Brenier & Frisch et al. (Month. Not. Roy. Ast. Soc. 346, 2003). In a neighborhood of merging singular structures in our examples, however, we show that reconstruction yielding a monotone Lagrangian map cannot be exact a.e., even off of the singularities themselves. |
| title | Analysis of the adhesion model and the reconstruction problem in cosmology |
| topic | Analysis of PDEs Mathematical Physics 35Q85, 85A40, 39A60, 49Q22, 34A60 |
| url | https://arxiv.org/abs/2511.09800 |