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

TL;DR

This paper proves global well-posedness for higher order KdV equations with dissipation in low regularity Sobolev spaces, showing optimality and smoothing effects for positive times.

Contribution

It establishes almost sharp global well-posedness results for dissipative dispersive equations on R in low regularity Sobolev spaces, highlighting optimality and smoothing.

Findings

Global well-posedness in low regularity Sobolev spaces

Flow-map not twice differentiable in rougher spaces

Solutions become smooth for positive times

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.