Unconditional well-posedness of fifth order KdV type equations with periodic boundary condition (Harmonic Analysis and Nonlinear Partial Differential Equations)

Abstract

This paper is announcement of the result obtained in [8] by Tsugawa and the author. We study the well-posedness of the Cauchy problem of the fifth order KdV type equations on T. We show the local well-posedness and unconditional uniqueness in Hs(T) for s ≥ 3/2. The main idea of the proof is using the conserved quantities to cancel the resonant parts with a loss of derivatives and applying the normal form reduction to the non-resonant parts to recover derivatives.