Gain of regularity for equations of KdV type
type: Item
instance of: scholarly article
title: Gain of regularity for equations of KdV type
zbMATH Open document ID: 0764.35021
DOI: 10.1016/S0294-1449(16)30243-8
author: Walter Craig
author: Walter A. Strauss
author: T. Kappeler
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1993-01-16T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78274
review text: Les auteurs montrent des résultats de régularité pour l'équation de Korteweg-de Vries nonlinéaire: \(\partial_ +u-f(\partial_ x^ 3 u,\partial_ x^ 2 u,\partial_ x u,u,x,t)=0\), \(f\) étant \(C^ \infty\). Si \(f\) vérifie \({\partial f\over\partial y_ 3}\geq c>0\) et \({\partial u \over \partial y_ 2}\leq 0\) (\(f(y_ 3,y_ 2,y,y_ 0,x,t)\)) ainsi que des propriètés sur elle et ses dérivées d'être bornée dans de bonnes-conditions, si, \(u\) vérifie une certaine régularité celle-ci peut-être améliorée (Théorèmes 2.1 et 2.2). Ils établissent également un théorème d'existence et d'unicité du problème de Cauchy associé (Théorème 3.2).
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
zbMATH DE Number: 93901
zbMATH Keywords: regularity
reviewed by: Marie-Therese Lacroix
MaRDI profile type: Publication
cites work: Solutions of the Korteweg-de Vries equation from irregular data
cites work: Local Smoothing Properties of Dispersive Equations
cites work: Linear dispersive equations of Airy type
cites work: Q4694012
cites work: Q3485349
cites work: Smoothing effect for some Schrödinger equations
cites work: On solutions of the initial value problem for the nonlinear Schrödinger equations in one space dimension
cites work: On solutions on the initial value problem for the nonlinear Schrödinger equations
cites work: Q3342896
cites work: Regularity of solutions to nonlinear dispersive equations
cites work: Regularity of solutions to the Schrödinger equation
description: scientific article; zbMATH DE number 93901