Regularizing effects in a linear kinetic equation for cubic interactions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914637056835584 |
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| author | Escobedo, Miguel |
| author_facet | Escobedo, Miguel |
| contents | We describe regularizing effects in the linearization of a kinetic equation that arises in study of a system of nonlinear waves satisfying the Schrödinger equation in terms of weak turbulence and condensate. The problem is first considered in spaces of bounded functions with weights, where existence of solutions and some first regularity properties are proved. After a suitable change of variables the equation is written in terms of a pseudo differential operator. Homogeneity of the equation and classical arguments of freezing of coefficients may then be used to prove regularizing effect in local Sobolev type spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05270 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularizing effects in a linear kinetic equation for cubic interactions Escobedo, Miguel Analysis of PDEs 45K05, 45A05, 45M05, 82C40, 82C05, 82C22 We describe regularizing effects in the linearization of a kinetic equation that arises in study of a system of nonlinear waves satisfying the Schrödinger equation in terms of weak turbulence and condensate. The problem is first considered in spaces of bounded functions with weights, where existence of solutions and some first regularity properties are proved. After a suitable change of variables the equation is written in terms of a pseudo differential operator. Homogeneity of the equation and classical arguments of freezing of coefficients may then be used to prove regularizing effect in local Sobolev type spaces. |
| title | Regularizing effects in a linear kinetic equation for cubic interactions |
| topic | Analysis of PDEs 45K05, 45A05, 45M05, 82C40, 82C05, 82C22 |
| url | https://arxiv.org/abs/2401.05270 |