Global well-posedness of initial-boundary value problem of fifth-order KdV equation posed on finite interval

We have established the existence and uniqueness of the local solution for partial derivative(t)u + partial derivative(5)(x)u - u partial derivative(x)u = 0, 0 < x < 1, t > 0,u(x,0) = phi (x), 0 < x < 1,u(0,t) = h(1)(t), u(1,t) = h(2)(t), partial derivative(x)u(1,t) = h(3)(t), (0,1)partial derivative(x)u(0,t) = h(4)(t), partial derivative(2)(x)u(1,t) = h(s)(t) t > 0,in the study of Zhao and Zhang [Non-homogeneous boundary value problem of the fifth-order KdV equations posed on a bounded interval , J. Math. Anal. Appl. 470 (2019), 251-278]. A question arises naturally: Can the local solution be extended to a global one? This article will address this question. First, through a series of logical deductions, a global a priori estimate is established, and then the local solution is naturally extended to a global solution.