From Kac particles to the Landau equation with hard potentials: BBGKY hierarchy method
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912537616842752 |
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| author | Guo, Shuchen |
| author_facet | Guo, Shuchen |
| contents | We study the Kac particle model for the space-homogenous Landau equation with hard potentials. By showing a sharper Povzner-type inequality, we obtain the uniform-in-time and uniform-in-N propagation of exponential moment for the first marginal of the solution of the many-particle Liouville equation. This key property enables us to show the uniqueness of weak solutions of the corresponding infinite Landau hierarchy by coupling method. As a result, we prove the propagation of chaos for the Landau equation with hard potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Kac particles to the Landau equation with hard potentials: BBGKY hierarchy method Guo, Shuchen Analysis of PDEs We study the Kac particle model for the space-homogenous Landau equation with hard potentials. By showing a sharper Povzner-type inequality, we obtain the uniform-in-time and uniform-in-N propagation of exponential moment for the first marginal of the solution of the many-particle Liouville equation. This key property enables us to show the uniqueness of weak solutions of the corresponding infinite Landau hierarchy by coupling method. As a result, we prove the propagation of chaos for the Landau equation with hard potentials. |
| title | From Kac particles to the Landau equation with hard potentials: BBGKY hierarchy method |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.10697 |