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On the well-posedness of the periodic KdV equation in high regularity classes


Kappeler, T; Pöschel, J (2008). On the well-posedness of the periodic KdV equation in high regularity classes. In: Craig, W. Hamiltonian dynamical systems and applications. Dordrecht: Springer, 431-441.

Abstract

We prove well-posedness results for the initial value problem of the periodic KdV equation 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 growth of Fourier coefficients, and ‘almost well posed’ in spaces with exponential growth of Fourier coefficients.

Abstract

We prove well-posedness results for the initial value problem of the periodic KdV equation 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 growth of Fourier coefficients, and ‘almost well posed’ in spaces with exponential growth of Fourier coefficients.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:09 Nov 2009 00:46
Last Modified:21 Nov 2017 14:20
Publisher:Springer
Series Name:NATO Science for Peace and Security Series B: Physics and Biophysics
ISSN:1874-6500
ISBN:978-1-4020-6962-8 (Print) 978-1-4020-6964-2 (Online)
Additional Information:Proceedings of the NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications, Montreal, Canada, 18-29 June 2007
Publisher DOI:https://doi.org/10.1007/978-1-4020-6964-2_18
Related URLs:http://www.poschel.de/pbl/well-posed-mon-1.pdf
http://www.poschel.de/pbl/well-posed-mon-2.pdf

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