The stochastic Korteweg-de Vries equation in \(L^2(\mathbb{R})\)
type: Item
instance of: scholarly article
title: The stochastic Korteweg-de Vries equation in \(L^2(\mathbb{R})\)
zbMATH Open document ID: 0927.35097
author: Jacques Printems
published in: Journal of Differential Equations
publication date: 1999-12-13T00:00:00Z
review text: The author presents two results of global existence and uniqueness of the Cauchy problem concerning the Korteweg-de Vries equation forced by random term of white noise type in the functional framework of weighted spaces on \(L^2(\mathbb{R})\). This work is motivated both by physical experiments where a forced generation of weakly nonlinear waves by localized disturbances was observed [see \textit{T. R. Akylas}, J. Fluid. Mech. 141, 455-466 (1984; Zbl 0551.76018) and \textit{S. J. Lee}, \textit{G. T. Yates} and \textit{T. Y. Wu}, J. Fluid. Mech. 199, 569-593 (1989)] and by a result of uniqueness in weighted space in the homogeneous case [see \textit{J. Ginibre} and \textit{Y. Tsutsumi}, SIAM J. Math. Anal. 20, No. 6, 1388-1425 (1989; Zbl 0702.35224), and \textit{S. N. Krushkov} and \textit{A. V. Faminskij}, Math. USSR, Sb. 48, 391-421 (1984; Zbl 0549.35104)].
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 1286236
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Korteweg-de Vries equation forced by random term of white noise type
reviewed by: Stanisław Wedrychowicz
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3548
OpenAlex ID: W2062262125
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DOI: 10.1006/JDEQ.1998.3548
description: scientific article; zbMATH DE number 1286236