Local well-posedness for the periodic korteweg-de vries equation in analytic gevrey classes

摘要

Motivated by the work of Gruji? and Kalisch, [Z. Gruji? 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.