Non-uniform dependence on periodic initial data for the two-component Fornberg-Whitham system in Besov spaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916375243522048 |
|---|---|
| author | Dutta, Prerona Keyfitz, Barbara Lee |
| author_facet | Dutta, Prerona Keyfitz, Barbara Lee |
| contents | This paper establishes non-uniform continuity of the data-to-solution map in the periodic case, for the two-component Fornberg-Whitham system in Besov spaces $B^s_{p,r}(\mathbb{T}) \times B^{s-1}_{p,r}(\mathbb{T})$ for $s> \max\{2+\frac{1}{p}, \frac{5}{2}\}$. In particular, when $p=2$ and $r=2$, this proves the non-uniform dependence on initial data for the system in Sobolev spaces $H^s(\mathbb{T})\times H^{s-1}(\mathbb{T})$ for $s> \frac{5}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-uniform dependence on periodic initial data for the two-component Fornberg-Whitham system in Besov spaces Dutta, Prerona Keyfitz, Barbara Lee Analysis of PDEs 35Q35, 35B30 This paper establishes non-uniform continuity of the data-to-solution map in the periodic case, for the two-component Fornberg-Whitham system in Besov spaces $B^s_{p,r}(\mathbb{T}) \times B^{s-1}_{p,r}(\mathbb{T})$ for $s> \max\{2+\frac{1}{p}, \frac{5}{2}\}$. In particular, when $p=2$ and $r=2$, this proves the non-uniform dependence on initial data for the system in Sobolev spaces $H^s(\mathbb{T})\times H^{s-1}(\mathbb{T})$ for $s> \frac{5}{2}$. |
| title | Non-uniform dependence on periodic initial data for the two-component Fornberg-Whitham system in Besov spaces |
| topic | Analysis of PDEs 35Q35, 35B30 |
| url | https://arxiv.org/abs/2407.04167 |