On the ill-posedness of kinetic wave equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910706927927296 |
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| author | Ampatzoglou, Ioakeim Léger, Tristan |
| author_facet | Ampatzoglou, Ioakeim Léger, Tristan |
| contents | In this article we identify a sharp ill-posedness/well-posedness threshold for kinetic wave equations (KWE) derived from quasilinear Schrödinger models. We show well-posedness using a collisional averaging estimate proved in our earlier work \cite{AmLe}. Ill-posedness manifests as instantaneous loss of smoothness for well-chosen initial data. We also prove that both the gain-only and full equation share the same well-posedness threhold, thus legitimizing a gain-only approach to solving 4-wave kinetic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12868 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the ill-posedness of kinetic wave equations Ampatzoglou, Ioakeim Léger, Tristan Analysis of PDEs Mathematical Physics In this article we identify a sharp ill-posedness/well-posedness threshold for kinetic wave equations (KWE) derived from quasilinear Schrödinger models. We show well-posedness using a collisional averaging estimate proved in our earlier work \cite{AmLe}. Ill-posedness manifests as instantaneous loss of smoothness for well-chosen initial data. We also prove that both the gain-only and full equation share the same well-posedness threhold, thus legitimizing a gain-only approach to solving 4-wave kinetic equations. |
| title | On the ill-posedness of kinetic wave equations |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2411.12868 |