Differential and Integral Equations

KdV and BO equations with bore-like data

Abstract

The global well-posedness of the initial-value problem associated to the Korteweg-de Vries equation with bore-like data is studied. In particular, we show that in the Sobolev space $H^s$, $s\ge 2$, the solutions of this problem remain bounded for any time. We also establish similar results for solutions of the initial-value problem associated to the Benjamin-Ono equation with this kind of data.

Article information

Source
Differential Integral Equations, Volume 11, Number 6 (1998), 895-915.

Dates
First available in Project Euclid: 30 April 2013