A priori bounds and equicontinuity of orbits for the intermediate long wave equation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913111563304960 |
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| author | Harrop-Griffiths, Benjamin Killip, Rowan Visan, Monica |
| author_facet | Harrop-Griffiths, Benjamin Killip, Rowan Visan, Monica |
| contents | We prove uniform-in-time a priori $H^s$ bounds for solutions to the intermediate long wave equation posed both on the line and on the circle, covering the range $-\frac12<s\leq0$. Additionally, we prove that the set of orbits emanating from a bounded and equicontinuous set in $H^s$ is also bounded and equicontinuous in $H^s$. Our proof is based on the identification of a suitable Lax pair formulation for the intermediate long wave equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23868 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A priori bounds and equicontinuity of orbits for the intermediate long wave equation Harrop-Griffiths, Benjamin Killip, Rowan Visan, Monica Analysis of PDEs We prove uniform-in-time a priori $H^s$ bounds for solutions to the intermediate long wave equation posed both on the line and on the circle, covering the range $-\frac12<s\leq0$. Additionally, we prove that the set of orbits emanating from a bounded and equicontinuous set in $H^s$ is also bounded and equicontinuous in $H^s$. Our proof is based on the identification of a suitable Lax pair formulation for the intermediate long wave equation. |
| title | A priori bounds and equicontinuity of orbits for the intermediate long wave equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.23868 |