On the energy transfer towards large values of wavenumbers for solutions of 4-wave kinetic equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913447005913088 |
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| author | Staffilani, Gigliola Tran, Minh-Binh |
| author_facet | Staffilani, Gigliola Tran, Minh-Binh |
| contents | Inspired by the fundamental work of Escobedo and Velazquez \cite{EscobedoVelazquez:2015:FTB,EscobedoVelazquez:2015:OTT}, we prove that solutions of 4-wave kinetic equations, under very general forms of the dispersion relations, exhibit the transfer of energy towards large values of wavenumbers as time evolves. We also provide a global well-posedness theory for mild solutions of the equation under general forms of the dispersion relations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the energy transfer towards large values of wavenumbers for solutions of 4-wave kinetic equations Staffilani, Gigliola Tran, Minh-Binh Mathematical Physics Inspired by the fundamental work of Escobedo and Velazquez \cite{EscobedoVelazquez:2015:FTB,EscobedoVelazquez:2015:OTT}, we prove that solutions of 4-wave kinetic equations, under very general forms of the dispersion relations, exhibit the transfer of energy towards large values of wavenumbers as time evolves. We also provide a global well-posedness theory for mild solutions of the equation under general forms of the dispersion relations. |
| title | On the energy transfer towards large values of wavenumbers for solutions of 4-wave kinetic equations |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2407.18508 |