LOCAL WELL-POSEDNESS OF THE FIFTH-ORDER KDV-TYPE EQUATIONS ON THE HALF-LINE

Abstract

This paper is a continuation of authors' previous work [6]. We extend the argument [6] to fifth-order KdV-type equations with different non-linearities, in specific, where the scaling argument does not hold. We establish the X-s,X-b nonlinear estimates for b < 1/2, which is almost optimal compared to the standard X-s,X-b nonlinear estimates for b > 1/2 [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.