  In this paper, we prove well-posedness of the Fornberg-Whitham equation in
Besov spaces $B_{2,r}^s$ in both the periodic and non-periodic cases. This will
imply the existence and uniqueness of solutions in the aforementioned spaces
along with the continuity of the data-to-solution map provided that the initial
data belongs to $B_{2,r}^s $. We also establish sharpness of continuity on the
data-to-solution map by showing that it is not uniformly continuous from any
bounded subset of $B_{2,r}^s$ to $C([-T,T]; B^s_{2,r})$. Furthermore, we prove
a Cauchy-Kowalevski type theorem for this equation that establishes the
existence and uniqueness of real analytic solutions and also provide blow-up
criterion for solutions.
