The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
type: Item
instance of: scholarly article
title: The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
zbMATH Open document ID: 0787.35090
DOI: 10.1215/S0012-7094-93-07101-3
author: C. E. Kenig
author: G. Ponce
author: L. Vega
published in: Duke Mathematical Journal
publication date: 1994-02-07T00:00:00Z
review text: The paper considers the initial value problem for the Korteweg-de Vries equation \[ u_ t+(u^ 2)_ x+u_{xxx}=0,\;t,x \in \mathbb{R},\;u(x,0)=u_ 0(x), \tag{1} \] for data in classical Sobolev spaces of negative order, i.e. \(u_ 0 \in H^{-s}(\mathbb{R})\) with \(s \geq 0\). The main result shows that the problem (1) is locally well posed for \(s<5/8\).
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35K30
zbMATH DE Number: 495434
zbMATH Keywords: initial value problem
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: locally well posed
reviewed by: Yuri S. Kivshar
MaRDI profile type: Publication
cites work: Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
cites work: Uniqueness of Solutions for the Generalized Korteweg–de Vries Equation
cites work: Solutions to the korteweg - devries equation with irregular initial profile
cites work: Q3342896
cites work: Q3974678
cites work: Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
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cites work: GENERALIZED SOLUTIONS OF THE CAUCHY PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION
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full work available at URL: s0012-7094-93-07101-3
OpenAlex ID: W1957427711
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description: scientific article; zbMATH DE number 495434