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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.20775 |
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| _version_ | 1866913933098483712 |
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| author | Alonso, Ricardo Gualdani, Maria Pia Sun, Weiran |
| author_facet | Alonso, Ricardo Gualdani, Maria Pia Sun, Weiran |
| contents | We introduce an $\mathcal{M}$-operator approach to establish the uniqueness of continuous or bounded solutions for a broad class of Landau-type nonlinear kinetic equations. The specific $\mathcal{M}$-operator, originally developed in [3], acts as a negative fractional derivative in both spatial and velocity variables and interacts in a controllable manner with the kinetic transport operator. The novelty of this method is that it bypasses the need for bounds on the derivatives of the solution - an assumption typically required in uniqueness arguments for non-cutoff equations. As a result, the method enables working with solutions with low regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Alonso, Ricardo Gualdani, Maria Pia Sun, Weiran Analysis of PDEs We introduce an $\mathcal{M}$-operator approach to establish the uniqueness of continuous or bounded solutions for a broad class of Landau-type nonlinear kinetic equations. The specific $\mathcal{M}$-operator, originally developed in [3], acts as a negative fractional derivative in both spatial and velocity variables and interacts in a controllable manner with the kinetic transport operator. The novelty of this method is that it bypasses the need for bounds on the derivatives of the solution - an assumption typically required in uniqueness arguments for non-cutoff equations. As a result, the method enables working with solutions with low regularity. |
| title | The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.20775 |