Local well posedness for KdV with data in a subspace of H^-1 and applications to illposedness theory for KdV and mKdV

2009/12/13 by Molinet, Luc, Wang, Baoxiang
#35Q53 #42 B 35. #46 E 35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0912.2480

Abstract

We prove the local well posedness for the KdV equation in the modulation space M^-1_2,1(ℝ). Our method is to substitute the dyadic decomposition by the uniform decomposition in the discrete Bourgain space. This wellposedness result enables us to show that the solution map is discontinuous at the origin with respect to the H^s -topology as soon as s

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