Local Well-Posedness in Critical Besov Spaces, Blow-Up Analysis, and Global Existence of Solutions for the B-Family Fokas-Olver-Rosenau-Qiao Equations

This work establishes the local well-posedness of the b-family Fokas-Olver-Rosenau-Qiao (bFORQ) equations in the critical Besov space B2, 15/2(R). We then analyze two special cases: For $b=1$, we prove finite-time blow-up of solutions with the explicit blow-up time T^* ≤ - 1/(ε u₀ₓ(x₁)m₀(x₁)); for $b=0$, we show the existence of global solutions in time.