Structured Continuity Equations in Fibred Wasserstein Spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915636553187328 |
|---|---|
| author | Bonnet-Weill, Benoît Duteil, Nastassia Pouradier |
| author_facet | Bonnet-Weill, Benoît Duteil, Nastassia Pouradier |
| contents | In this article, we develop a comprehensive ODE-theory for structured continuity equations in fibred probability spaces, which represent a class of heterogeneous PDEs arising as the meanfield limit nonexchangeable particle systems. After investigating in depth the topologies induced by the so-called fibred and classical Wasserstein metrics on such probability spaces, we establish quantitative Cauchy-Lipschitz and qualitative Carathéodory-Peano well-posedness results for structured continuity equations, along with precise correspondences between this class of evolutions, classical Lagrangian dynamics, and continuity equations. In keeping with what has long been known for exchangeable dynamics, we derive a general meanfield approximation result by solutions of nonexchangeable particle systems, along with a quantitative variant thereof under practically reasonable regularity assumptions on the driving field and initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19784 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structured Continuity Equations in Fibred Wasserstein Spaces Bonnet-Weill, Benoît Duteil, Nastassia Pouradier Analysis of PDEs Probability In this article, we develop a comprehensive ODE-theory for structured continuity equations in fibred probability spaces, which represent a class of heterogeneous PDEs arising as the meanfield limit nonexchangeable particle systems. After investigating in depth the topologies induced by the so-called fibred and classical Wasserstein metrics on such probability spaces, we establish quantitative Cauchy-Lipschitz and qualitative Carathéodory-Peano well-posedness results for structured continuity equations, along with precise correspondences between this class of evolutions, classical Lagrangian dynamics, and continuity equations. In keeping with what has long been known for exchangeable dynamics, we derive a general meanfield approximation result by solutions of nonexchangeable particle systems, along with a quantitative variant thereof under practically reasonable regularity assumptions on the driving field and initial data. |
| title | Structured Continuity Equations in Fibred Wasserstein Spaces |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2511.19784 |