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Non-uniform dependence on periodic initial data for the two-component Fornberg-Whitham system in Besov spaces
- Publication Year :
- 2024
-
Abstract
- 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 $s> \frac{5}{2}$.
- Subjects :
- Mathematics - Analysis of PDEs
35Q35, 35B30
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2407.04167
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3934/math.20241234