Classical Solutions of the Fornberg-Whitham Equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913718064906240 |
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| author | Burkhalter, Georgia Thompson, Ryan C. Waldrep, Madison |
| author_facet | Burkhalter, Georgia Thompson, Ryan C. Waldrep, Madison |
| contents | In this paper, we prove well-posedness in $C^1(\mathbb{R})$ (a.k.a. classical solutions) of the Fornberg-Whitham equation. To achieve this objective, we study its weak formulation under a Lagrangian framework. Applying the fundamental theorem of ordinary differential equations to the generated semi-linear system, we then construct a unique solution to the equation that is continuously dependent on the initial data. These results improve upon others in Sobolev and Besov spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08159 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Classical Solutions of the Fornberg-Whitham Equation Burkhalter, Georgia Thompson, Ryan C. Waldrep, Madison Analysis of PDEs 35Q53 In this paper, we prove well-posedness in $C^1(\mathbb{R})$ (a.k.a. classical solutions) of the Fornberg-Whitham equation. To achieve this objective, we study its weak formulation under a Lagrangian framework. Applying the fundamental theorem of ordinary differential equations to the generated semi-linear system, we then construct a unique solution to the equation that is continuously dependent on the initial data. These results improve upon others in Sobolev and Besov spaces. |
| title | Classical Solutions of the Fornberg-Whitham Equation |
| topic | Analysis of PDEs 35Q53 |
| url | https://arxiv.org/abs/2212.08159 |