The lifespan of small data solutions for intermediate long wave equation (ILW)

Abstract

This article represents a first step toward understanding the long time dynamics of solutions for the intermediate long wave equation (ILW). While this problem is known to be both completely integrable and globally well-posed in H32, much less seems to be known concerning its long time dynamics. Here we prove well-posedness at much lower regularity, namely an L2 global well-posedness result. Then we consider the case of small and localized data and show that the solutions disperse up to cubic timescale.

Locations

• Communications in Partial Differential Equations - View
• arXiv (Cornell University) - View - PDF