KdV and BO equations with bore-like data
type: Item
instance of: scholarly article
title: KdV and BO equations with bore-like data
zbMATH Open document ID: 1022.35059
published in: Differential and Integral Equations
publication date: 2003-01-26T00:00:00Z
review text: The authors prove the global well-posedness of the initial value problem for the Korteweg-de Vries (KdV) equation with initial conditions of a special type. These are functions \(g\) satisfying { (i)} \( g(x) \to C_\pm \) as \(x\to \pm \infty \), { (ii)} \( g'\in H^s\) for some \(s\geq 0\), { (iii)} \( (g-C_+)\in L^2(0,\infty)\), \((g-C_-)\in L^2(-\infty ,0)\). Similar conclusions are derived for the solutions of the Benjamin-Ono (BO) equation.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35G25
zbMATH DE Number: 1858731
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: Benjamin-Ono equation
zbMATH Keywords: global well-posedness
zbMATH Keywords: bore-like initial data
author: Rafael José jun. Iorio
author: Felipe Linares
author: M. Scialom
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1858731