On the wellposedness of the KdV/KdV2 equations and their frequency maps

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Abstract
In form of a case study for the KdV and the KdV2 equations, we present a novel approach of representing the frequencies of integrable PDEs which allows to extend them analytically to spaces of low regularity and to study their asymptotics. Applications include convexity properties of the Hamiltonians and wellposedness results in spaces of low regularity. In particular, it is proved that on \mathcal{H}^{s} the KdV2 equation is C^{0} -wellposed if s⩾0 and illposed (in a strong sense) if s < 0 .
Funding Information
  • Swiss National Science Foundation
  • Swiss National Science Foundation

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