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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.00267 |
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| _version_ | 1866913813978152960 |
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| author | Escobedo, Miguel |
| author_facet | Escobedo, Miguel |
| contents | The existence of local, classical solutions is proved, for a system of two coupled equations that describe, in the framework of the wave turbulence theory, the fluctuations around an equilibrium, of a system of nonlinear waves satisfying the 3-d cubic Schrödinger equation, weakly interacting in presence of a condensate. The function that describes the density of waves behaves like a singular Rayleigh Jeans equilibria near the origin, and induces a strictly increasing behavior in time of the function describing the condensate's density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local classical solutions of a kinetic equation for three waves interactions in presence of a Dirac measure at the origin Escobedo, Miguel Analysis of PDEs The existence of local, classical solutions is proved, for a system of two coupled equations that describe, in the framework of the wave turbulence theory, the fluctuations around an equilibrium, of a system of nonlinear waves satisfying the 3-d cubic Schrödinger equation, weakly interacting in presence of a condensate. The function that describes the density of waves behaves like a singular Rayleigh Jeans equilibria near the origin, and induces a strictly increasing behavior in time of the function describing the condensate's density. |
| title | Local classical solutions of a kinetic equation for three waves interactions in presence of a Dirac measure at the origin |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.00267 |