Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2506.20775 |
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Inhaltsangabe:
- 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.