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On the periodic KdV equation in weighted Sobolev spaces


Kappeler, T; Pöschel, J (2009). On the periodic KdV equation in weighted Sobolev spaces. Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, 26(3):841-853.

Abstract

We prove well-posedness results for the initial value problem of the periodic KdV equation as well as Kam type results in classes of high regularity solutions. More precisely, we consider the problem in weighted Sobolev spaces, which comprise classical Sobolev spaces, Gevrey spaces, and analytic spaces. We show that the initial value problem is well posed in all spaces with subexponential decay of Fourier coefficients, and ‘almost well posed’ in spaces with exponential decay of Fourier coefficients.

Abstract

We prove well-posedness results for the initial value problem of the periodic KdV equation as well as Kam type results in classes of high regularity solutions. More precisely, we consider the problem in weighted Sobolev spaces, which comprise classical Sobolev spaces, Gevrey spaces, and analytic spaces. We show that the initial value problem is well posed in all spaces with subexponential decay of Fourier coefficients, and ‘almost well posed’ in spaces with exponential decay of Fourier coefficients.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:May 2009
Deposited On:05 Nov 2009 12:45
Last Modified:05 Apr 2016 13:31
Publisher:Elsevier
ISSN:0294-1449
Publisher DOI:https://doi.org/10.1016/j.anihpc.2008.03.004
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2526404

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