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

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 Bˢp,r(T) × Bˢ⁻¹p,r(T) for s> max\2+1/p, 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 Hˢ(T)× Hˢ⁻¹(T) for s> 5/2.