Local well-posedness for the periodic Korteweg-de Vries equation in analytic Gevrey classes

Qifan Li

doi:10.3934/cpaa.2012.11.1097

Article Contents

2012, Volume 11, Issue 3: 1097-1109. Doi: 10.3934/cpaa.2012.11.1097

This issue Previous Article Low regularity well-posedness for the 3D Klein - Gordon - Schrödinger system Next Article Remarks on a two dimensional BBM type equation

Local well-posedness for the periodic Korteweg-de Vries equation in analytic Gevrey classes

Qifan Li^1,

1.
Department of Mathematics, University of Bergen, 5008 Bergen

Received: October 31, 2010

Revised: January 31, 2011

Published: April 2012

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Abstract

Motivated by the work of Grujić and Kalisch, [Z. Grujić and H. Kalisch, Local well-posedness of the generalized Korteweg-de Vries equation in spaces of analytic functions, Differential and Integral Equations 15 (2002) 1325--1334], we prove the local well-posedness for the periodic KdV equation in spaces of periodic functions analytic on a strip around the real axis without shrinking the width of the strip in time.

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Mathematics Subject Classification: Primary: 35Q53; Secondary: 35A07.

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References

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