On the Korteweg-de Vries limit for the Boussinesq equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909166424031232 |
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| author | Hong, Younghun Yang, Changhun |
| author_facet | Hong, Younghun Yang, Changhun |
| contents | The Korteweg-de Vries (KdV) equation is known as a universal equation describing various long waves in dispersive systems. In this article, we prove that in a certain scaling regime, a large class of rough solutions to the Boussinesq equation are approximated by the sums of two counter-propagating waves solving the KdV equations. It extends the earlier result by \cite{Schneider1998} to slightly more regular than $L^2$-solutions. Our proof is based on robust Fourier analysis methods developed for the low regularity theory of nonlinear dispersive equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Korteweg-de Vries limit for the Boussinesq equation Hong, Younghun Yang, Changhun Analysis of PDEs 35Q53, 76B15 The Korteweg-de Vries (KdV) equation is known as a universal equation describing various long waves in dispersive systems. In this article, we prove that in a certain scaling regime, a large class of rough solutions to the Boussinesq equation are approximated by the sums of two counter-propagating waves solving the KdV equations. It extends the earlier result by \cite{Schneider1998} to slightly more regular than $L^2$-solutions. Our proof is based on robust Fourier analysis methods developed for the low regularity theory of nonlinear dispersive equations. |
| title | On the Korteweg-de Vries limit for the Boussinesq equation |
| topic | Analysis of PDEs 35Q53, 76B15 |
| url | https://arxiv.org/abs/2403.16648 |