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

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} $.

Keywords

• fornberg-whitham system
• besov space
• non-uniform dependence