JournalsaihpcVol. 26, No. 3pp. 841–853

On the periodic KdV equation in weighted Sobolev spaces

  • Jürgen Pöschel

    Institut für Analysis, Dynamik und Optimierung, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

  • Thomas Kappeler

    Universität Zürich, Institut für Mathematik, Winterthurerstrasse 66, Zürich, Switzerland
On the periodic KdV equation in weighted Sobolev spaces cover
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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.

Cite this article

Jürgen Pöschel, Thomas Kappeler, On the periodic KdV equation in weighted Sobolev spaces. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 3, pp. 841–853

DOI 10.1016/J.ANIHPC.2008.03.004