On the Cauchy Problem for the Dispersion Generalized Camassa-Holm Equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911877555027968 |
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| author | Ayhan, Nesibe Mutlubas, Nilay Duruk |
| author_facet | Ayhan, Nesibe Mutlubas, Nilay Duruk |
| contents | In this paper, we establish local well-posedness of the Cauchy problem for a recently proposed dispersion generalized Camassa-Holm equation by using Kato's semigroup approach for quasi-linear evolution equations. We show that for initial data in the Sobolev space $H^{s}(\mathbb{R})$ with $s>\frac{7}{2}+p$, the Cauchy problem is locally well-posed, where $p$ is an even real number determined by the order of the positive differential operator $L$ corresponding to the dispersive effect added to the Camassa-Holm equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15443 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Cauchy Problem for the Dispersion Generalized Camassa-Holm Equation Ayhan, Nesibe Mutlubas, Nilay Duruk Analysis of PDEs Primary: 35G25, 35L30, 47D60, Secondary: 35B65, 47D03 In this paper, we establish local well-posedness of the Cauchy problem for a recently proposed dispersion generalized Camassa-Holm equation by using Kato's semigroup approach for quasi-linear evolution equations. We show that for initial data in the Sobolev space $H^{s}(\mathbb{R})$ with $s>\frac{7}{2}+p$, the Cauchy problem is locally well-posed, where $p$ is an even real number determined by the order of the positive differential operator $L$ corresponding to the dispersive effect added to the Camassa-Holm equation. |
| title | On the Cauchy Problem for the Dispersion Generalized Camassa-Holm Equation |
| topic | Analysis of PDEs Primary: 35G25, 35L30, 47D60, Secondary: 35B65, 47D03 |
| url | https://arxiv.org/abs/2309.15443 |