Blow-up phenomena and the local well-posedness of a Two-Component b-Family Equations in Besov spaces

In this paper, we first establish the local well-posednesss of a Two-Component b-Family equations in nonhomogeneous Besov spaces $B_{p,1}^{1+\frac{1}{p}}$ with $1\le p<+\mathrm{\infty }\mathrm{.}$ Then we present a new blow-up result for the Two-Component b-Family equations.