Almost Sharp Global Well-Posedness for a class of Dissipative and Dispersive Equations on R in Low Regularity Sobolev Spaces

Abstract

In this paper we obtain global well-posedness in low order Sobolev spaces of higher order KdV type equations with dissipation. The result is optimal in the sense that the flow-map is not twice continuously differentiable in rougher spaces. The solution is shown to be smooth for positive times.

This paper has been withdrawn by the author due to several errors