Well-posedness of KdV type equations

Abstract

In this work, we study the initial value problems associated to some linear perturbations of KdV equations. Our focus is in the well-posedness issues for initial data given in the L^2-based Sobolev spaces. We develop a method that allows us to treat the problem in the Bourgain's space associated to the KdV equation. With this method, we can use the multilinear estimates developed in the KdV context, thereby getting analogous well-posedness results for linearly perturbed equations.

Keywords

• Initial value problem
• well-posedness
• Bourgain spaces,
• KdV equation