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.

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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3 citations in Web of Science®
3 citations in Scopus®

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English May 2009 05 Nov 2009 12:45 05 Apr 2016 13:31 Elsevier 0294-1449 10.1016/j.anihpc.2008.03.004 http://www.ams.org/mathscinet-getitem?mr=2526404
Permanent URL: http://doi.org/10.5167/uzh-23484