Finite time energy cascade for mixed $3-$ and $4-$wave kinetic equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908728207343616 |
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| author | Staffilani, Gigliola Tran, Minh-Binh |
| author_facet | Staffilani, Gigliola Tran, Minh-Binh |
| contents | In this work we study a kinetic equation whose collision operator comprises three distinct wave interaction mechanisms: one representing a 3-wave process, and two corresponding to 4-wave processes. This wave kinetic equation describes the temporal evolution of the density function of the thermal cloud of a finite temperature trapped Bose gas. We establish that, for a broad class of initial data, solutions exhibit an immediate cascade of energy towards arbitrarily large frequencies. Furthermore, for other classes of initial conditions, we demonstrate that the energy is transferred to infinity in finite time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite time energy cascade for mixed $3-$ and $4-$wave kinetic equations Staffilani, Gigliola Tran, Minh-Binh Mathematical Physics Analysis of PDEs In this work we study a kinetic equation whose collision operator comprises three distinct wave interaction mechanisms: one representing a 3-wave process, and two corresponding to 4-wave processes. This wave kinetic equation describes the temporal evolution of the density function of the thermal cloud of a finite temperature trapped Bose gas. We establish that, for a broad class of initial data, solutions exhibit an immediate cascade of energy towards arbitrarily large frequencies. Furthermore, for other classes of initial conditions, we demonstrate that the energy is transferred to infinity in finite time. |
| title | Finite time energy cascade for mixed $3-$ and $4-$wave kinetic equations |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2512.19531 |