Sharp well--posedness for the generalized KdV of order three on the half line

Erin Leigh Compaan; Nikolaos Tzirakis

doi:10.1016/j.physd.2019.132208

paper

Sharp well--posedness for the generalized KdV of order three on the half line

arXiv:1902.07161 · doi:10.1016/j.physd.2019.132208

Abstract

In this paper we study the generalized Korteweg de Vries (KdV) equation with the nonlinear term of order three: $(u^{3 + 1})_{x}$ . We prove sharp local well--posedness for the initial and boundary value problem posed on the right half line. We thus close the gap in the well--posedness theory of the generalized KdV which remained open after the seminal work of Colliander and Kenig in \cite{CK}.

31 pages