Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929499543699456 |
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| author | Sastre-Gómez, Silvia |
| author_facet | Sastre-Gómez, Silvia |
| contents | In this work we prove the equivalence between three different weak formulations of the steady periodic water wave problem where the vorticity is discontinuous. In particular, we prove that generalised versions of the standard Euler and stream function formulation of the governing equations are equivalent to a weak version of the recently introduced modified-height formulation. The weak solutions of these formulations are considered in Hölder spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity Sastre-Gómez, Silvia Analysis of PDEs In this work we prove the equivalence between three different weak formulations of the steady periodic water wave problem where the vorticity is discontinuous. In particular, we prove that generalised versions of the standard Euler and stream function formulation of the governing equations are equivalent to a weak version of the recently introduced modified-height formulation. The weak solutions of these formulations are considered in Hölder spaces. |
| title | Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.08720 |