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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.17082 |
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| _version_ | 1866912775964459008 |
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| author | Junné, Jonathan Winter, Raphael Yoldaş, Havva |
| author_facet | Junné, Jonathan Winter, Raphael Yoldaş, Havva |
| contents | We consider the spatially homogeneous Landau equation for multiple species with different masses. As in the single-species case, the singularity of the collision operator is determined by a parameter $γ\in [-3,1]$, where $γ= -3$ corresponds to Coulomb interactions. We prove that if $γ\geq -\sqrt{8}$ in the cross-interaction operators, then there exists a natural multi-species generalization of the Fisher information which is a Lyapunov functional for the multi-species Landau system. On the other hand, we give a counterexample showing that the Fisher information is in general no longer a Lyapunov functional below the threshold $(γ< - \sqrt{8})$ for the two-species system if one species has infinite mass. However, we are able to provide a new method to show global well-posedness, by constructing a different Lyapunov functional based on the spherical Fisher information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17082 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence of solutions to the multi-species Landau equation Junné, Jonathan Winter, Raphael Yoldaş, Havva Analysis of PDEs Mathematical Physics 35Q70, 82C40, 58J35 We consider the spatially homogeneous Landau equation for multiple species with different masses. As in the single-species case, the singularity of the collision operator is determined by a parameter $γ\in [-3,1]$, where $γ= -3$ corresponds to Coulomb interactions. We prove that if $γ\geq -\sqrt{8}$ in the cross-interaction operators, then there exists a natural multi-species generalization of the Fisher information which is a Lyapunov functional for the multi-species Landau system. On the other hand, we give a counterexample showing that the Fisher information is in general no longer a Lyapunov functional below the threshold $(γ< - \sqrt{8})$ for the two-species system if one species has infinite mass. However, we are able to provide a new method to show global well-posedness, by constructing a different Lyapunov functional based on the spherical Fisher information. |
| title | On the existence of solutions to the multi-species Landau equation |
| topic | Analysis of PDEs Mathematical Physics 35Q70, 82C40, 58J35 |
| url | https://arxiv.org/abs/2512.17082 |