Global existence and decay of small solutions in a viscous half Klein-Gordon equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916952247631872 |
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| author | Garénaux, Louis de Rijk, Björn |
| author_facet | Garénaux, Louis de Rijk, Björn |
| contents | We establish global existence and decay of solutions of a viscous half Klein-Gordon equation with a quadratic nonlinearity considering initial data, whose Fourier transform is small in L1 cap Linfty. Our analysis relies on the observation that nonresonant dispersive effects yield a transformation of the quadratic nonlinearity into a subcritical nonlocal quartic one, which can be controlled by the linear diffusive dynamics through a standard L1 - Linfty argument. This transformation can be realized by applying the normal form method of Shatah or, equivalently, through integration by parts in time in the associated Duhamel formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global existence and decay of small solutions in a viscous half Klein-Gordon equation Garénaux, Louis de Rijk, Björn Analysis of PDEs We establish global existence and decay of solutions of a viscous half Klein-Gordon equation with a quadratic nonlinearity considering initial data, whose Fourier transform is small in L1 cap Linfty. Our analysis relies on the observation that nonresonant dispersive effects yield a transformation of the quadratic nonlinearity into a subcritical nonlocal quartic one, which can be controlled by the linear diffusive dynamics through a standard L1 - Linfty argument. This transformation can be realized by applying the normal form method of Shatah or, equivalently, through integration by parts in time in the associated Duhamel formula. |
| title | Global existence and decay of small solutions in a viscous half Klein-Gordon equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.13188 |