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arXiv · 2407.04167

Non-uniform dependence on periodic initial data for the two-component Fornberg-Whitham system in Besov spaces

Prerona Dutta·Barbara Lee Keyfitz
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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 $s> \frac{5}{2}$.

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Prerona Dutta, Barbara Lee Keyfitz. 2024-07-04. Non-uniform dependence on periodic initial data for the two-component Fornberg-Whitham system in Besov spaces. https://doi.org/10.3934/math.20241234

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