Well-posedness and non-uniform dependence on initial data for the Fornberg–Whitham-type equation in Besov spaces.

In this paper, we first establish the local well-posedness for the Fornberg–Whitham-type equation in the Besov spaces B p , r s (R) with 1 ≤ p , r ≤ ∞ and s > m a x { 1 + 1 p , 3 2 } , which improve the previous work in Sobolev spaces H s (R) = B 2 , 2 s (R) with s > 3 2 (Lai and Luo in J Differ Equ 344:509–521, 2023). Furthermore, we prove the solution is not uniformly continuous dependence on the initial data in the Besov spaces B p , r s (R) with 1 ≤ p ≤ ∞ , 1 ≤ r < ∞ and s > m a x { 1 + 1 p , 3 2 } . [ABSTRACT FROM AUTHOR]