Weakly nonlinear models for hydroelastic water waves
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910084037083136 |
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| author | Alonso-Orán, Diego Granero-Belinchón, Rafael Ziebell, Juliana S. |
| author_facet | Alonso-Orán, Diego Granero-Belinchón, Rafael Ziebell, Juliana S. |
| contents | In this work, we derive reduced interface models for hydroelastic water waves coupled to a nonlinear viscoelastic plate. In a weakly nonlinear small-steepness regime we obtain bidirectional nonlocal evolution equations capturing the interface dynamics up to quadratic order, and we also derive two unidirectional models describing one-way propagation while retaining the leading dispersive and dissipative effects induced by the plate. Remarkably, one of the bidirectional model has a doubly nonlinear structure in the sense that there there is a nonlinear elliptic operator acting on the acceleration of the interface. We prove local well-posedness for the bidirectional model for small data via a two-parameter regularization and nested fixed points. For the unidirectional models, we obtain local well-posedness for arbitrary data and global well-posedness for small data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27802 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weakly nonlinear models for hydroelastic water waves Alonso-Orán, Diego Granero-Belinchón, Rafael Ziebell, Juliana S. Analysis of PDEs Mathematical Physics Fluid Dynamics In this work, we derive reduced interface models for hydroelastic water waves coupled to a nonlinear viscoelastic plate. In a weakly nonlinear small-steepness regime we obtain bidirectional nonlocal evolution equations capturing the interface dynamics up to quadratic order, and we also derive two unidirectional models describing one-way propagation while retaining the leading dispersive and dissipative effects induced by the plate. Remarkably, one of the bidirectional model has a doubly nonlinear structure in the sense that there there is a nonlinear elliptic operator acting on the acceleration of the interface. We prove local well-posedness for the bidirectional model for small data via a two-parameter regularization and nested fixed points. For the unidirectional models, we obtain local well-posedness for arbitrary data and global well-posedness for small data. |
| title | Weakly nonlinear models for hydroelastic water waves |
| topic | Analysis of PDEs Mathematical Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2603.27802 |