This paper is a continuation of authors’ previous work . We extend the argument  to fifth-order KdV-type equations with different nonlinearities, in specific, where the scaling argument does not hold. We establish the X s,b nonlinear estimates for b < 1 2 , which is almost optimal compared to the standard X s,b nonlinear estimates for b > 2 1 [8, 17]. As an immediate conclusion, we prove the local well-posedness of the initial-boundary value problem (IBVP) for fifth-order KdV-type equations on the right half-line and the left half-line.
- Fifth-order KdV-type equations
- Initial-boundary value problem
- Local well-posedness