The fuzzy Landau equation: global well-posedness and Fisher information
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915449984253952 |
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| author | Gualdani, Maria Pia Guillen, Nestor Pavlović, Nataša Tasković, Maja Zamponi, Nicola |
| author_facet | Gualdani, Maria Pia Guillen, Nestor Pavlović, Nataša Tasković, Maja Zamponi, Nicola |
| contents | We study a fuzzy variant of the inhomogeneous Landau equation and establish global-in-time existence and uniqueness of smooth solutions for moderately soft potentials. The spatial delocalization introduced in the collision operator not only enhances regularity and prevents singularity formation, but also reveals additional structural properties of the model. In particular, we show that several forms of the Fisher information decay monotonically or remain uniformly bounded in time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_08689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The fuzzy Landau equation: global well-posedness and Fisher information Gualdani, Maria Pia Guillen, Nestor Pavlović, Nataša Tasković, Maja Zamponi, Nicola Analysis of PDEs Mathematical Physics 35A01, 82D05, 82C40, 76N10, 35Q20 We study a fuzzy variant of the inhomogeneous Landau equation and establish global-in-time existence and uniqueness of smooth solutions for moderately soft potentials. The spatial delocalization introduced in the collision operator not only enhances regularity and prevents singularity formation, but also reveals additional structural properties of the model. In particular, we show that several forms of the Fisher information decay monotonically or remain uniformly bounded in time. |
| title | The fuzzy Landau equation: global well-posedness and Fisher information |
| topic | Analysis of PDEs Mathematical Physics 35A01, 82D05, 82C40, 76N10, 35Q20 |
| url | https://arxiv.org/abs/2507.08689 |