Long time justification of wave turbulence theory
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917632368705536 |
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| author | Deng, Yu Hani, Zaher |
| author_facet | Deng, Yu Hani, Zaher |
| contents | In a series of previous works (arXiv:2104.11204, arXiv:2110.04565, arXiv:2301.07063), we gave a rigorous derivation of the homogeneous wave kinetic equation (WKE) up to small multiples of the kinetic timescale, which corresponds to short time solutions to the wave kinetic equation. In this work, we extend this justification to arbitrarily long times that cover the full lifespan of the WKE. This is the first large data, long-time derivation ever obtained in any nonlinear (particle or wave) collisional kinetic limit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_10082 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Long time justification of wave turbulence theory Deng, Yu Hani, Zaher Analysis of PDEs Mathematical Physics 35Q82 (Primary) 35Q55, 82C10 (Secondary) In a series of previous works (arXiv:2104.11204, arXiv:2110.04565, arXiv:2301.07063), we gave a rigorous derivation of the homogeneous wave kinetic equation (WKE) up to small multiples of the kinetic timescale, which corresponds to short time solutions to the wave kinetic equation. In this work, we extend this justification to arbitrarily long times that cover the full lifespan of the WKE. This is the first large data, long-time derivation ever obtained in any nonlinear (particle or wave) collisional kinetic limit. |
| title | Long time justification of wave turbulence theory |
| topic | Analysis of PDEs Mathematical Physics 35Q82 (Primary) 35Q55, 82C10 (Secondary) |
| url | https://arxiv.org/abs/2311.10082 |