Global Well-posedness of the Viscous b-Family of Equations

In this paper,the global well-posedness of the viscous b-family equations are stud- ied. Get the global existence and uniqueness of solution to the viscous b-family equation for u0 2 L 2 (R). According to the energy estimate, we result the local well-posedness for u0 2 L 2 (R).By using this theorem and the usual extension theory the global well-posedness is proved.